/sqt/ /qtddtot/- stupid questions thread

[Anonymous No.11159921]

Previously >>11146370

[Anonymous No.11159966]

How do I solve these type of questions? Keeps giving me 0.

[Anonymous No.11159983]

>>11159966
Numerical underflow? Try writing out the Taylor series for exp(x) and computing the first few terms.

[Anonymous No.11159995]

>>11155821
Bless you too.

Unanswered questions from the previous thread:

Maths questions, exact subject in brackets:
>>11147487 [Complex analysis.]
>>11149157 [Basic rep theory of Lie algebras]
>>11150489 [High school algebra.]
>>11151710 [Binomial theorem.]
>>11155228 [It looks like a recursive definition for a series of functions.]
>>11156173 [Introductory real analysis.]
>>11158090 [Graphs.]
>>11159332 followed by >>11159346 and finally >>11159365 [Real analysis.]
>>11159872 [Polynomials.] (Yes.)

Physics questions, exact subject in brackets:
>>11146463 [Thermo 1.]
>>11147127 [Antimatter.]
>>11155503 [Virtual particles.]

Engineering:
>>11148587
>>11158609

Computer science:
>>11148734
>>11156404
>>11157324 [Specifically Latex.]

Alchemy questions:
>>11146904

Chemistry questions:
>>11149681

Geography questions:
>>11152385

Stupid questions:
>>11147107
>>11147160
>>11148384
>>11149023
>>11149309 (No.)
>>11149440
>>11153064
>>11155060
>>11155883
>>11155914
>>11158450 [Was answered for maths as PDEs.]

[Anonymous No.11160008]

>>11159966
it halves every 1620 years and there is 120g, halving would be multiplying by 0.5, but this is every 1620 years, we need to find the amount it decreases by every year, lets make an equation for this, x is the multiplier for a single year, 120 would half to 60 every 1620 years, this means that 120 would multiply by x^1620 to become 60, 120 * x^1620 = 60, devide both sides by 120, x^1620 = 0.5, root 1620 both sides, x = 1620th root of 0.5, we will keep the number like this for a more accurate result, now we make nth term for the decrease of 120 for n amount of years, 120 is multiplied by the 1620th root of 0.5 for every year so 120 * (1620th root of 0.5)^n, replace n with 100 and we get our answer, 114.9738694g

[Anonymous No.11160034]

>>11159966
120 * (1/2)^(100/1620) = 114.97

[Anonymous No.11160038]

Today is a great day
It's a day of learning math
In this happy place

[Anonymous No.11160078]

>>11160008
>>11160034
So why is e in the equation?

[Anonymous No.11160091]

>>11159995
>>11159872
Some basic reasoning
Let [math] p(x),q(x)\in R[x] [/math] and [math] \Delta [/math] be a root of [math] p(x)=0 [/math]. Then [math] p(\Delta)=0[/math]. Since [math] p(x)|q(x) [/math] there exists some [math] g(x)\in R[x] [/math] such that [math] q(x)=p(x)g(x) [/math]. Now [math] q(\Delta)=g(\Delta)p(\Delta)=0 [/math].

[Anonymous No.11160106]

>>11159966
Not going to do it, but in the second sentence you solve for k in y=y0e^-kt (you know how y and y0 are related when t=1620). In the last sentence you substitute in those values into the equation you have found.

[Anonymous No.11160107]

Any idea what I'm doing wrong here?
The answers should be 30, 24.1, 150, and 155.9.
Perhaps I should try solve for sin, since it is asking for positive angles in 1st and 2nd quadrant?

[Anonymous No.11160113]

>>11160107
line 6 is wrong. Should be
24sin^2xcos^2x - 1 = 14sin^2 x

[Anonymous No.11160116]

>>11160107
The whole solutions is fucked up, learn to think.
sin^2 2x = 1 - cos^2 2x
You get a quadratic equation. Solve it.

[Anonymous No.11160171]

>>11159995
> >>11159332 followed by >>11159346 and finally >>11159365 [Real analysis.]
This one seems to have been answered in /mg/.

>>11151710 [Binomial theorem.]
We can interpret the standard binomial formula
[eqn] (1+x)^n = 1 + nx + \frac{n(n-1) }{2!} x^2 + \frac{n(n-1)(n-2) }{3!} x^3 + \ldots + \frac{ n(n-1) \cdots (n-r+1) }{r!} x^r + \ldots[/eqn]
as a Taylor series expansion in x (for a fixed n), which is valid even when n is not an integer.
For example, when n = -1 this becomes
1/(1+x) = 1 - x + x^2 - x^3 + ...
and you may recognize the geometric series by making the substitution [math]x \mapsto -x[/math].
A common application of this is in calculus, where you can rewrite the integrand as an infinite sum (ideally a polynomial in x) and integrate termwise.
The catch, of course, is that this is only valid for x when the series converges, which is why we're interested in the range.

E.g. for the geometric series example above, the range of validity is |x| < 1, which is unchanged if we substitute with -x. But if we substituted [math] x \mapsto 100x[/math], say, this would shrink the range of validity to |100x| < 1 i.e. -10 < x < 10.

[Anonymous No.11160173]

>>11160171
Errata: Last line should be -1/100 < x < 1/100.
I should really proofread my stuff more often.

[Anonymous No.11160175]

>>11160116
Thanks anon. I tried to solve it like that the first time, but I made a mistake.

[Anonymous No.11160246]

Given that water evaporates at 100ºC, when I accidentally drop some water on my kitchen counter/floor/table, why does it disappear after a few hours tops? Or when someone dries their hair, what the fuck happens to the water? None of those situations involve that high of a temperature

Also, when you turn on a fan inside a closed room, why does the air get cooler instead of hotter? You're turning electric energy into kinetic and supposedly heat is released so what gives?

[Anonymous No.11160269]

>>11160246
Evaporation.
It doesn't get cooler, you just have wind on your face.

[Anonymous No.11160275]

>>11160246
While the internal energy U of given amount of water is a function its temperature, it should be noted that "temperature" only makes sense as an average. That is, temperature only makes sense when you are talking about the average of the kinetic energies of ~10^23 many molecules or more. So, you can say that internal energy is a function of the average kinetic energy of each molecule. But the kinetic energies of these molecules follow a Boltzmann distribution, and some have just enough to breach the liquid surface of the water you spilled and join the other water vapor in the air.

tl;dr: temperature is like the average energy of some water, which means some tiny amount of water molecules will have just a little bit more energy and can vaporize

[Anonymous No.11160279]

>>11160246
Maxwell Boltzmann distribution of kinetic energies of the water molecules, random pressure and moisture fluctuations in the air.

[Anonymous No.11160291]

I'm very ambitious but can never back it up with a proper study routine. I've never found school hard either, but since I lack discipline what generally happens is when subjects pile up I have to scrape by to get decent grades and always end up feeling regretful because I realize I lost yet another opportunity for learning.
Is there hope for fried dopamine receptors?

[Anonymous No.11160414]

>>11146463
Cengel and Boles
>>>11158609
Yes, that's right
>>>11152385
Geology, meteorology

[Anonymous No.11160442]

has celestialgirlfriendfag finally been rangebanned?

[Anonymous No.11160524]

I just sorta need a sanity check here. Is pic related correct, or am I flawed somehow? Both theta a and theta b are time-dependent.

[Anonymous No.11160584]

Let p_1, ..., p_n be arbitrary different primes. Let [math](a_n)_{n\in \mathbb{R}}[/math] and [math](b_n)_{n\in \mathbb{R}}[/math] be arbitrary real sequences such that [math]\prod_{i=1}^n (|a_i|+|b_i|)\neq 0[/math]. Let f: R->R with [math]f(x) = \sum_{i=1}^n \left(a_i\cos\left(\frac{2\pi x}{p_i}\right)+b_i\sin\left(\frac{2\pi x}{p_i}\right)\right)[/math]. How do I show that f(x)=0 has at least [math]\frac{\prod_{i=1}^n p_i}{\sum_{i=1}^n p_i}[/math] roots in [0,T] where T is one period of f?

I really hope the tex works out.

[Anonymous No.11160594]

>>11160524
Wrong. d/dt ( cos(theta_b - theta_a))= (d/dt (theta_b))(-sin(theta_b - theta_a). Chain rule, you have to bring out a factor of thetadot.

[Anonymous No.11160598]

>>11160524
Is it [math]cos [ (\theta _b - \theta a)( \dot \theta _b + \dot \theta _a)][/math] or [math][cos (\theta _b - \theta a)]( \dot \theta _b + \dot \theta _a)[/math]?

[Anonymous No.11160659]

>>11160598
I apologize for the poor formatting. It should be [math][cos (\theta _b - \theta a)]( \dot \theta _b + \dot \theta _a)[/math], however now I'm realizing it is wrong because of what >>11160594 is saying. Thanks.

[Anonymous No.11160679]

Is Remi smarter than Eirin?

[Anonymous No.11160841]

is it true that [math] |a - b| \geq |b| - |a|[/math]? can ya prove it?

[Anonymous No.11160849]

>>11160841
>>11160841
hint: | a | = | b + (a-b) |

[Anonymous No.11160905]

>>11159995
Some of these I have already answered. Specifically >>11149157 and >>11147127. However the posts seemed to be deleted by quality-hating jannies but you can check out my answer by referencing the replies to it.
>>11155503
By definition, virtual particles are unobservables that oscillate beyond the energy scale of the problem; in other words, they're the "inner edges" of the Feynman diagrams. For instance, radiative corrections all stem from exchange of virtual particles which make QED amplitudes diverge in the IR limit. They oscillate with wavenumber much beyond those restricted by momentum conservation across the vertices.
>>11160679
No.

[Anonymous No.11160914]

>>11160442
one can hope, but it seems unlikely
rangebans are reserved for people who make it their life's mission to destroy a board, not just ordinary shit users

[Anonymous No.11160943]

>>11160679
Maybe, but im smarter than both ;3

[Anonymous No.11161040]

>>11160943
doubt.jpg

[Anonymous No.11161090]

Why does evaporation naturally occur in water, when the steam pressure at room temperature is much lower than the atmospheric pressure?

[Anonymous No.11161117]

>>11161090
See
>>11160275

[Anonymous No.11161217]

>>11160679
Probably not.
>>11160905
Cross referencing answers would take a millenium, are you insane?
>>11160943
Now this I'm certain is false.

[Anonymous No.11161221]

>>11161217
Use 4chanX, child.

[Anonymous No.11161634]

>>11159921
What field in physics would be the smartest to enter in to? What would be the worst one? Is there a field in it that always needs new people or is the whole work force a competitive bloodbath where if you didn't go to some prestigious school then you are doomed?

[Anonymous No.11161681]

>>11161634
>Is there a field in it that always needs new people or is the whole work force a competitive bloodbath where if you didn't go to some prestigious school then you are doomed?

I assume you're talking about an academic career.

The latter but with less weight than you think on the prestigious school. Academia is overcrowded and underpaid because there exists a surplus of overzealous candidates that would be overqualified for a lot of other jobs but love what they are doing too much to pursue another career. Unless you're unregrettably nuts about the subject, pursuing a career in academia(or even just a PhD) in math/physics is objectively a bad life choice. You would be competing with literal autists that do nothing else. If you belong to that group go for it. If you want to have a more traditional life don't go down that path.

[Anonymous No.11161722]

On a resume, should i include a project i worked on that was part of a lab course? We designed an antenna using software and then fabricated it. I’d like to add it to my resume to beef it up

[Anonymous No.11161806]

>>11161221
>child
I'll have you know I'm nineteen and a quarter, thank you very much.

[Anonymous No.11161821]

>>11161806
you're still a kid, kid

[Anonymous No.11161832]

>>11161806
>im older than someone on here
i suppose its time to pack my things, then

[Anonymous No.11161849]

Where can I get a cute nerd bf?
I want to touch him while he tries to do math

[Anonymous No.11161859]

>>11161806
a baby!
>>11161849
grindr

[Anonymous No.11161868]

>>11161859
But I want a stem nerd
Grindr is full of normies
The more awkward and introvert the better

[Anonymous No.11161948]

>>11161868
have you tried looking for fellow gays at your school?

[Anonymous No.11161952]

>>11159921
do i need addy if i'm gonna make it?

[Anonymous No.11161963]

>>11161952
Don't do addy. No really, don't.

[Anonymous No.11162127]

copypasted from another thread
if we had a glass of salt water stored somewhere for a few days, would the ions move to the top/bottom or would they be distributed uniformly?

[Anonymous No.11162133]

>>11162127
They would remain evenly distributed. If they were not evenly distributed, you would have pockets with net charge which would end up dispersing the ions by electrical forces anyway. So they remain distributed evenly.

[Anonymous No.11162142]

Is there anywhere I can find the Lagrangian for an undamped, undriven triple pendulum? Textbooks, articles, websites, anywhere?

[Anonymous No.11162146]

>>11162127
over or under saturating should be considered

[Anonymous No.11162156]

>>11162133
that makes sense

>>11162146
under saturated, like seawater

[Anonymous No.11162202]

>>11162142
Im working on it

[Anonymous No.11163035]

Here's a stupid grade level question I'm having trouble with. The problem is straightforward until part e, why is there a discrepancy in area?

[Anonymous No.11163062]

>>11163035
because in (a) you're assuming it's a triangle
but it's not a triangle, since the yellow and red triangles have different slopes

[Anonymous No.11163111]

Hi I'm studying group theory and I came across this question.
Define [math]G_1=\{1,2,3,4\}[/math] and define [math]*[/math] so that [math]a*b=a\times b \pmod 5[/math], for all [math]a,b\in G_1[/math]. What is [math]2^{-1}[/math]?
I'm not sure how I'm supposed to approach this question tho. The hint given to me was for [math]x^n[/math] where [math]n<0[/math], [math]x^{-1}*x^{n+1}[/math]

[Anonymous No.11163118]

>>11163062
Ah, I see. The power of suggestion. I notice now he actually never called the colored region a right triangle even in part a. Thanks.

[Anonymous No.11163123]

>>11163111
Remember how in a finite group some finite power of a equals the inverse?
Literally just that.
There are, however, less retarded ways of doing this.
Like trying every other element of the group.
Tip: 2x3=6 cong 1 mod 5.

[Anonymous No.11163178]

>>11163123
Thanks anon I appreciate your help.
I still don't quite get negative exponents though. For positive exponents I could just trace it out on on the Cayley table but I'm not sure what to do for this situation.

[Anonymous No.11163187]

>>11163178
>trace it out on the Cayley table
You can find inverses on the Cayley table.
Suppose you want x^-1. Find the x collumn.Find the identity in the x collumn. Trace out what row it's in. That's x^-1.
For x^-n, you use (x-1)^n or (x^n)^-1 depending on what's immediately easier.

[Anonymous No.11163194]

>>11163187
FUCK. I'm retarded I didn't realize they were asking for the inverse.
Thanks a bunch.

[Anonymous No.11163506]

what does pic related mean?

[Anonymous No.11163549]

>>11163506
space of continuous functions in the interval [0,2]

[Anonymous No.11163550]

>>11163549
ty

[Anonymous No.11163914]

Why Math Is Important In Life?

[Anonymous No.11163915]

>>11163914
who told you that?

[Anonymous No.11163936]

>>11163915
your mother

[Anonymous No.11163974]

CHEM NOOB
Could anyone help me with this extraction process. So I use EtOAc to isolate the organic layer. Then do I add EtOAc to the aqueous layer, separate and isolate the organic layer again and repeat. Then do I combine all the organic layers?

[Anonymous No.11163983]

>>11163936
why would she tell you such a thing?

[Anonymous No.11164062]

>>11159921
Does anyone know what the capital R stands for in this formula? I can't seem to find the formula anywhere even if I Google the name for it and its really starting to bug me.

[Anonymous No.11164087]

>>11163983
because she knew you will ask me such a question

[Anonymous No.11164088]

can music increase your IQ?

[Anonymous No.11164089]

anyone have a recommendation for a good intro botany book? I have a strong bio/chem background. I'll probably just grab something random off libgen

[Anonymous No.11164115]

>>11164088
IQ is a worthless metric. Learning to play an instrument, however, it certainly good for your mind.

[Anonymous No.11164178]

Do you guys have a recommendation for a physics and information theory textbook(i.e. information theory from the physical side, information in statistical physics, quantum physics, blackholes etc.)?

[Anonymous No.11164226]

>>11163974
Yes

[Anonymous No.11164438]

>>11163506
follow up:
how the heck do i do this? how do you take the inner product of two functions?

[Anonymous No.11164455]

>>11164438
[eqn]\langle f(t),g(t)\rangle=\int_1^2f(t)\cdot g(t)\text{ d}t[/eqn]
where 1 and 2 are the bounds of the interval

[Anonymous No.11164461]

>>11164455
and that dot in the middle of the functions in the integral is just multiplication?

[Anonymous No.11164462]

>>11164461
yes

[Anonymous No.11164478]

>>11164462
ok, ty judy poster

[Anonymous No.11164484]

Anyone know how I can sketch the last equation?

[Anonymous No.11164510]

>>11164455
>that latex
Watch me:
[math]<f, g> = \int_0^2 fg ~ dt[/math]

[Anonymous No.11164513]

>>11164510
yikes, dude

[Anonymous No.11164525]

>>11164455
>even the differential is typeset correctly
very nice butters

[Anonymous No.11164538]

>>11164525
ty, i try

[Anonymous No.11164677]

>>11159921
why are smug demon girls so comfy?

[Anonymous No.11164727]

>>11164455
ok, what about this one?

[Anonymous No.11164730]

>>11164727
i dont know what that notation means. find the norm of x^2 on some interval? if that's the case, you would compute the inner product of x^2 with itself on the given interval, and then take the square root.

[Anonymous No.11164731]

>>11164730
im pretty sure it means magnitude
>you would compute the inner product of x^2 with itself on the given interval, and then take the square root
that sounds about right

[Anonymous No.11164733]

>>11164731
magnitude is a kind of norm ;3 but yes, my explanation is how you would find the "magnitude" of x^2 on the given interval

[Anonymous No.11164735]

>>11164731
>>11164733
that's how you would find the "magnitude" of any continuous function on an interval, btw. the "take the square root" part has nothing to do with the fact that the function in question is x^2

[Anonymous No.11164737]

>>11164733
>>11164735
right, tyvm fren

[Anonymous No.11164739]

>>11164737
yw <3 i wish i new more lin alg

[Anonymous No.11164747]

Can someone recommend me some books about industrial processes for waste management?

[Anonymous No.11164994]

While working with your main math problems, can you relax by switching to recreational math problems? Does it even work or your brain has limited mana?

[Anonymous No.11165030]

I've been reading up on compound extraction from plant materials, and I have yet to ind a summary of quite how this process can be divided, either by types of compounds to be extracted, or by method of extraction.

It seems to me that the compounds fall largely into 3 categories, alkaloids, phenols and volatile oils. The latter seems to have straight methods, though the use the entire plant part, thus the phenols and alkaloids might go to waste. Penols can be mostly extracted with alcohol and a few other common solvents, whereas alkaloids are the trickiest substance, usually requiring removing just about anything which isn't an alkaloid.

How wrong am I, and how is extraction from plant material usually structured?

[Anonymous No.11165206]

>>11159921
How can I make protein hydrolysates at home?

[Anonymous No.11165484]

>>11164994
sure you can. think of working out and then doing some light cardio.

[Anonymous No.11165486]

Why can't I throw it in the trash?

[Anonymous No.11165694]

I read somewhere that space is not an emptiness (I know there are particles and gases, but like really far apart, right?), but actually "something". It was compared to water, as a tangible thing. Unfortunately, the post didn't elaborate on that and I haven't found anything else drawing explaining anything similar or makings this comparison. Does anyone know what it could be refering to?

I have just discovered that the warm-hot intergalactic medium is a thing, but could it really be this the reference for the statement? I probably am wrong, but it is my (very superficial) understanding that it is gaseous, so I am not sure if it can be compared to water.

Thanks in advance.

[Anonymous No.11165750]

For auto-didacts, how structured is your study?

When I was studying Axler precalc, I would go section to section, chapter to chapter, and do every problem and just move on with no self-imposed quizzes or review. It worked, I learned pre-calculus, but I would get often get burnt out when I had the intention to study every day.

For single variable calculus I found two university syllabi using the well-written but not widely used textbook I'm reading, and I'm following their assigned homework, doing their end chapter quizzes, studying their worksheets and review, and doing their exams(with self-imposed time limits) and I find it much easier to study math daily and I actively recall and use the information I learned. Is that common?

syllabi in case you're wondering
>http://fractal.math.unr.edu/~ejolson/181-14/
>http://pi.math.cornell.edu/~web1220/

[Anonymous No.11165754]

>>11165694
Sounds like aetherposting.
https://en.m.wikipedia.org/wiki/Luminiferous_aether
Could also be a reference to general relativity, but the language is weird.
>>11165750
I study what I want to, forget it in a few months, study it again, and recall everything for long periods of time.
I also usually glance through the end of chapter exercises.

[Anonymous No.11165756]

>>11165694
Maybe they're talking about the Dirac sea, which is apparently equivalent to the modern postulation of antimatter (antiparticles).
Though I'm not a physicsfag so you might want to get a second opinion on that.

[Anonymous No.11165767]

>>11165754
>>11165756

First of all, thanks for answering. I will check both suggestions, which seem like an entertaining reading.

Also, excuse my weird language. I was writing in a rush and didn't check my post.

Pic unrelated.

[Anonymous No.11165789]

>>11165750
Everybody is different. Almost everyone benefits from _some_ amount of structure, so in that regard your experience is very common.
Whether you need only a very loose structure or you do better going full-blown micromanaged autism or something in the middle is up to your temperament.

A lot of structure doesn't work for me personally. I sit down with a rough plan of what things I need to learn today and then I start reading about them. When I feel like I understand something decently I do some related problems.

[Anonymous No.11165804]

>>11156404
Yeah it seems to follow the good basics of AI, agents, constrains, uncertainty; the only doubt I have is on the Machine Learning part which seems a bit advanced for a basic course on AI.
If you want to read something else that is good as well I suggest "AI a modern approach" by Russel & Norvig.
I'll leave downloading and proof to the reader as an exercise.

[Anonymous No.11165816]

>>11147107
No, no one carries genes for any particular man or woman, you just carry them because you inherited them.
>>11147160
Probably not, mammals would have not become so dominant without that particular mass extinction event.
>>11148384
Specifically, we mostly don't know. In general we know that the neurons fire each other all the time and do stuff, we also know that some specifics parts of the brain do some specifics tasks, but some other parts can start doing those things if the brain is damaged.
>>11149440
This goes beyond the knowledge of a man.
>>11153064
I suggest you ask a doctor in this field, or a group of doctors.
>>11155883
No, aliens are chilling in their post singularity sauna right now, they don't give a shit about your planet.
>>11155914
I suggest asking to 3 different deacons about this and see if their answers go one against the other.
>>11158450
Not a physics, but I can guess that making a "Theory of Everything" is pretty hard.

[Anonymous No.11166029]

what does this mean?

[Anonymous No.11166030]

>>11166029
depends on context. could mean the partial derivative of f wrt n, could mean the nth component of a vector called f, could mean the nth term in a sequence called f. impossible to tell from just that.

[Anonymous No.11166034]

>>11166030
this is the whole question
also if someone can help answer this i would appreciate

[Anonymous No.11166037]

>>11166034
f is a sequence. how are you studying induction and you dont know this?

[Anonymous No.11166038]

>>11166029
The n-th function in a sequence squared, most likely.
>>11166034
We'll need at least the definition of f_n.

[Anonymous No.11166044]

>>11166037
i just skimmed through the chapter
got finals in 2-3 weeks ;_;

[Anonymous No.11166070]

>>11166038
>We'll need at least the definition of f_n.
Looks like the Fibonacci numbers f(-1)=f(0)=1, f(1)=2, f(2)=3, f(3)=5 etc.

[Anonymous No.11166095]

>>11166038
>We'll need at least the definition of f_n.
That's the recurrence for the Fibonacci numbers [math]f_{n+1} = f_n + f_{n-1}[/math].
Then, letting L(n) denote the LHS, we have
[eqn]L(n) = f_{n+1}f_{n-1} - f_n^2 = (f_n + f_{n-1})f_{n-1} - f_n^2 \\ = f_n(f_{n-1} - f_n) + f_{n-1}^2 \\ = - ( f_nf_{n-2} - f_{n-1}^2) \\ = -L(n-1)[/eqn]
Which we can think of as a geometric series with scale factor -1, and then induct down to the RHS (-1)^n.

[Anonymous No.11166248]

what are some functions that show difference between methods of interpolations? I mean functions where linear Interpolation gives vastly different results that polynomial interpolation?

[Anonymous No.11166288]

>>11166248
The exponential function, the logarithm function, the sigmoid, the smooth bump function, etc.
The last two should be particularly explicit.

[Anonymous No.11166366]

>>11166095
>>11166095
thanks, im the girl that posted the question

[Anonymous No.11166506]

>>11166288
what do you mean i tried with bump function:
[math]
e^{1-\frac{1}{1-x^2}}
[/math]
and i got pic related. Difference is only at the ends of domain.

[Anonymous No.11166523]

can you guys post more 2hus please?

[Anonymous No.11166553]

>>11166506
Expand the domain, foolish fool.

[Anonymous No.11166565]

>>11166553
You mean take x from [-10:10] for example? But this function returns 0 for everything smaller than -1 and bigger than 1, so what can I achieve with that?

[Anonymous No.11166577]

>>11166565
Listen, do you want the example or not?

[Anonymous No.11166583]

>>11166577
please tell me what i should do? I use C with GSL library for interpolation, and gnuplot for visualisation

[Anonymous No.11166587]

>>11166583
>how do I numerically implement it
>>>/g/sqt
It is honestly in subject, I just doubt someone here will actually answer.

[Anonymous No.11166599]

for the graph of a power series, what the fuck is actually being plotted? x? n? something else?

[Anonymous No.11166600]

http://tutorial.math.lamar.edu/Classes/CalcII/IntegralTest.aspx

>go through half the page
>don't understand shit
>author then puts a 3 line summary that literally explains the whole concept

why?

[Anonymous No.11166606]

>>11166587
its ok, i just need function that gives vastly different result interpolated by polynomials than by splines/linear. Just a function, or do you think something wrong with my implementation?

[Anonymous No.11166611]

I just hate measure theory. Shit is so confusing. I feel like a brainlet

[Anonymous No.11166623]

If a projectile was heated rapidly mid-flight and it melted, would its velocity be affected?

[Anonymous No.11166624]

>>11166599
Its graphing a(x)

[Anonymous No.11166627]

>>11166623
yes

[Anonymous No.11166638]

>>11166627
would it make it faster or slower?

[Anonymous No.11166640]

>>11166623
No
>>11166627
What? How does adding heat change momentum

[Anonymous No.11166643]

>>11166640
Drag would be different on the solid and liquid projectiles.

[Anonymous No.11166647]

>>11166643
Sure, I suppose. But the phase change itself is not the cause of the ΔV

[Anonymous No.11166656]

>>11165694
They could have been referring to the zero-point energy of the vacuum.

[Anonymous No.11166663]

Why am I so fucking stupid

[Anonymous No.11166668]

what should I read after Gödel, Escher and Bach?

[Anonymous No.11166711]

What am I going to make with this recipe?
>>11166663
You are not trying hard enough, I know you can do it

[Anonymous No.11166743]

Does anyone have that meme where a child asks his father why 1+1=2 and he thinks of a rigorous proof?

[Anonymous No.11166787]

Is there a specific meaning to class numbers? Like, what differentiates a 100 level course from a 200 level course past the latter being more advanced?
Is it based on the year in your undergrad you would typically take it?

[Anonymous No.11166788]

>>11166787
More or less yeah

[Anonymous No.11166806]

>>11166647
>But the phase change itself is not the cause of the ΔV
lol

[Anonymous No.11166807]

>>11166806
lol

[Anonymous No.11166817]

>>11166807
heh

[Anonymous No.11166821]

>>11166523
Sure.
>>11166606
Lad, polynomials are polynomials. If you look at it's behavior outside the domain of definition, it just explodes. Further, by just expanding the domain you'll see some really strange behavior (that you'd expect from a polynomial).
>>11166668
Pic related.
>>11166711
Just google the ingredients.
>salt
>vinegar
>lemon juice
>bleach
>copper
>CO2

[Anonymous No.11166827]

Are "impossible" things like finding closed forms of most antiderivatives and differential equations impossible because of the way we have constructed our methods of mathematics, or are they inherently, intrinsically impossible to solve regardless of the basis or substrata with which the problems are presented

>inb4 numerical solutions
don't be a goof you know what I mean

[Anonymous No.11166867]

Let [math]R [/math] be an integral domain with identity and let [math]\mathbb{F}[/math] be the field of fractions of R. We can consider R as a subring of [math]\mathbb{F}[/math] in the canonical way via the map [math]r \mapsto (r,1)[/math]. Let S be a subring of [math]\mathbb{F}[/math] containing R. I need to prove that the field of fractions of S is isomorphic to [math]\mathbb{F}[/math], but I'm struggling with doing this... At first I tried constructing an injective ring homomorphism from R to the field of fractions of S, but the induced map [math]\mathbb{F} \righarrow \text{frac}(S)[/math] is not an isomorphism.. could anyone help me out with this?

[Anonymous No.11166869]

>>11166867
Oops, meant [math]\mathbb{F} \rightarrow \text{frac}(S)[/math] for those who didn't understand that.

[Anonymous No.11166876]

>>11166821
Thanks anon! Do you think it produces lots of gas?

[Anonymous No.11166897]

how do I stop feeling like I'm imposing or being an inconvenience during office hours

[Anonymous No.11166899]

>>11166827
The notion of a closed form is essentially arbitrary, you know.
It's not even like getting the solution in term of logarithms, exponentials, polynomials and roots makes it possible or easier to evaluate by hand, you're really just delaying the use of numerical methods.
>>11166867
Use the universal property.
>>11166876
Oh yeah, definitely, but you'll get a nice little portal filled with pretty crystals.

[Anonymous No.11166910]

If girls smell good because of pheromones, why haven't we isolated those pheromones and sold them in bulk to apply to unpleasent things (or like sex toys I guess too)?

[Anonymous No.11166929]

>>11166910
human pheromones doesn't real

[Anonymous No.11166940]

>>11166897
Realize that internal angst and low self esteem in combination with trivial questions that indicate a lack of effort and interest in the class all serve to embitter the instructor against you every time you show up at their office
>>11166910
>because of pheromones
they don’t

[Anonymous No.11166953]

>>11166899
Thanks for the reply. I'm >>11166867

The induced map via the universal property is not an isomorphism though my nigga, so I'm not sure where to go from there:/

[Anonymous No.11166962]

>>11166953
Replied in /mg/.

[Anonymous No.11167118]

is the universe just a loop?

[Anonymous No.11167122]

>>11167118
there is not evidence for that

[Anonymous No.11167206]

Brainlet here, how is group theory used in physics and how are laws of physics deduced from symmetry? is there a way to construct some kind of toy universe from a "small" group and figure out what all the particles and laws that universe would have? if a toy universe could be made, why don't we instantly know all the physical properties of all particles and molecules in our own universe? and not just proton/neutron particles, but maybe particles made with "new-protons" that are made out of strange/top quarks instead of up quarks

I dont really even know what im asking with all that, but basically just how can I derive some/all laws of a universe given a group. Like, if our universe has some certain group structure in it, then i instantly know carbon can accept 4 different bonds.

[Anonymous No.11167855]

I'm planning on doing a CS degree next year at uni, but I need to learn Algebra through to Calculus because I failed math in high school. I'm not dumb or anything, I just really hated doing it as a teenager. Do you think it's possible to learn all that math by using Khan Academy by at least July next year? Also, what else can I do to get a head start on a CS degree?

[El Arcón No.11167862]

woah hey guys what's going on in here

[Anonymous No.11167878]

>>11167122
I get it

>my gf made dinner

>now I'm going to ram raid a house again

thats why

because otherwise I wouldn't have to ram raid a house

>or shopping center

[Anonymous No.11168001]

Do I need to study a book on proofs or logic before I tackle on book like Spivak/Apostol? Or can I just jump in and wing it?

Anyway to learn how to prove organically?

[Anonymous No.11168766]

>>11167878
>le schizophrenia
>>11168001
No, you can jump in

[Anonymous No.11168894]

I am your average engineering student, not a super whiz at math but not shit either.
That being said, is it a bad idea for me to take Calc III and DiffEq the same semester, if they're the only two classes I'll take?

[Anonymous No.11168911]

>>11166611
For X to be real-valued is the same as saying that [math]|X|^p[/math] is [math] \left[ 0, \infty\right)[/math]-valued.
Additionally, by substitution the RHS integral can be shown to be
[eqn]\int_0^\infty P(|X|\geq t) pt^{p-1} dt \\ = \int_0^\infty P( |X|^p \geq t^p) dt^p \\ = \int_0^\infty P(|X|^p \geq x) dx[/eqn].

So the statement to be shown is a special case of the identity
[eqn]E[Y] = \int_0^\infty P(Y \geq x)dx \quad \text{ for non-negative }Y[/eqn]
where Y = |X|^p.

There's a visual intuition for why this works, using Fubini's theorem (pic related), but it's probably easier to start with [math]Y = \int_0^\infty \mathbb{1}_{x \leq Y}(x) dx[/math] (where [math]\mathbb{1}[/math] is a characteristic function so the area to be integrated is a rectangle with height 1 and width Y) and integrate both sides.

[Anonymous No.11168915]

>>11168911
attaching pic

[Anonymous No.11168927]

how do I obtain a function y(x) which satisfies the following condition:
y=\int_{0}^{x}y*x^{2}dx

[Anonymous No.11168941]

>>11168894
I have no idea what's up with americans. I'm literally juggling 5 classes from my bachelors, one class from the postgraduate program for the sake of it and a part-time job, and it's comfy enough for me to take a break and shitpost here, and a good number of my classmates have full time jobs and still take at least three classes. You niggas go "what if I take this one mildly hard class can I take anything else in the semester will a ghost kill me?"
>>11168927
Integrate the right side by parts to gouge out both x's.

[Anonymous No.11169176]

>>11168911
>>11168915
Thanks a lot! your explanation was really helpful. I guess I need to go back and revise substitutions and common integral solving techniques.
I kind of struggle with the shortcuts that professors take when they manipulate what "comes after the d" in an integral, like when you want to change measure inside of one.
Also expressing functions in terms of indicator functions and manipulating them doesn't come naturally to me.
I guess I need to study more. Thanks again

[Anonymous No.11169187]

Let object A have no traits. Keep in mind that "having no traits", "existing", and "not existing" are all traits according to common intuition.

Pls help im relly confused what object A is, ive banged my head on it with logic for about a year now and i just get these iterative recursions that break at every step, im having some progress using non traditional logics/semantics. But im really really confused still

[Anonymous No.11169233]

>>11169187
Schrödinger's cat
Object exist and not exist like cat in box
But object not like cat and like cat, so box in box
Object is box in box
Quantum box
>>11167862
The usual. Answering questions, shitposting, studying.
>>11167206
>how is group theory used in physics and how are laws of physics deduced from symmetry
They usually aren't deduced entirely from the symmetries, you also have some aditional results, like "an object's path has velocity everywhere timelike". Special relativity is a really good example and a lot more accessible than you'd think, I'd recommend just picking it up.
Classical mechanics is, in a certain way, "too intuitive" to make the use of symmetries explicit.
The entire remainder of the post is really weird, I'd honestly recommend just learning special relativity.

[Anonymous No.11169251]

>>11169233
I thought of something like that but it still has issues, like "existing and not existing" is still a trait. It could potentially have non traits, or be on a smear between existence and nonexistence so its trait is undefinable and thus isnt effected by definite logic.

One thing that really bugs me though is, im unsure if this object even matters. I dont know a way to phrase this without upsetting its definition, but... just cause it contradicts itself, why does itself have to be extant in the first place. I have some thought about, since it perturbs the system of my mind and now yours, its "attempted to exist," but the truth is, at least with just logic, any attempted perturbation of the mind is something other than it - a confusion, error, or string of text. And so it never perturbs my mind. Yet, how am i talking about it?

One insight I had was I can say, "object A does not perturb any system". In that case, the paradox is deleted from existence because it never perturbed my mind to begin with

Yet, still theres the intuition that its something extant, and the definition for object A prevents it from not perturbing my mind, because it cant have the trait of not perturbing my mind (or not perturbing any sentient/existence generating system). But I wonder, what is the weight of a definition anyway

I also feel like a better comprehension of ontology and the nature of words like existence, reality, nonexistence would help

[Anonymous No.11169258]

https://youtu.be/J3FcbFqSoQY in this video guy performs on himself gene therapy to cure his lactose intolerance. Will he be able to do the same thing, but with genes that in charge of IQ level (when scientists will discover them)?

[Anonymous No.11169271]

>>11169233
In desperation, I did a google search and this popped up:
>Definition of meaningless. 1 : having no meaning especially : lacking any significance. 2 : having no assigned function in a language system.
That bit about "no assigned function in a language system" is really useful. Something can easily have no traits in a given subset of reality, by not perturbing a system within reality. Which then leads me to realize I can redefine object A as... "that which does not perturb reality itself". The issue here is, how can I prove that the two definitions are isomorphic? The prior definition, which I'd been using for a year seems to have some sort of glitch that this one doesn't, and that glitch is a lot of what bugs me. The other thing is, with this new definition, again, if object A doesn't perturb reality, how am I thinking about it?

[Anonymous No.11169345]

>>11169187
simply talking about this object has given it a trait. one cannot talk about, think about, or conceptualise this object

[Anonymous No.11169379]

>>11169345
if your object has a trait it is not the object in question

if the object is untalkaboutable then it has the untalkaboutability trait and is not object A, because object A has no traits

[Anonymous No.11169396]

>>11159921
I really enjoy Algebra and kinda enjoy (algebraic and point set) topology.
Complex analysis 1 was super beautiful, measure theory is nice.

Now I may want to dig into algebraic geometry in two semesters and the professor suggested that before I do so I should take Algebra 2 (no prob), algebraic topology, differential geometry and riemann surfaces, of the latter three I have only time for two at max.
alg topo and diffgeo will be taught again when I plan to take the algebraic geometry course, riemann surfaces is not scheduled any time soon.

any suggestions which courses I should take and which might be "enough" to autodidactically study pretty superficially?

in terms of abstraction I'd say algtopo2 > riemann > algtopo 1 > diffgeo

[Anonymous No.11169415]

>>11169396
Honestly, Riemann Surfaces will be a solid 90% of your intuition for algebraic geometry, Differential Geometry will be 5%, and Algebraic Topology is genuinely necessary for computations and the remaining 5% of intuition.
If the idea is superficial study, absolutely go for Riemann Surfaces. Donaldson is good.

[Anonymous No.11169469]

>>11169379
>dude language paradoxes

[Anonymous No.11169480]

>>11169469
Language can be isomorphic to pure logic, so its a logical paradox. Does that make you feel better? Either way, abstractions are an accessible part of reality, even if only through symbols and how they feel in our heads. If there's a glitch with that, there's a glitch with reality or our symbol systems.

[Anonymous No.11169482]

>>11169480
There is nothing wrong with our symbols. All logical schema are inconsistent or incomplete or both.

[Anonymous No.11169490]

>>11169482
Are you saying symbols are distinct from schema? Why are all logical schema inconsistent or incomplete or both?

[Anonymous No.11169541]

>>11169490
No I'm not. Because of Gödels theorems.

[Anonymous No.11169549]

>>11169541
If our schemas are inconsistent, that means the symbols carry inconsistent meanings, so our symbols have an issue. More importantly, imo, is that if our schemas are incomplete, we lack symbols for certain ideas.

[Anonymous No.11169553]

>>11169549
We've done our damndest to make sure low level logic is consistent. It is probably not inconsistent, but it is incomplete. It cannot deal with language paradoxes. They aren't very interesting.

[Anonymous No.11169556]

>>11168941
EU and American credit hours aren't the same anon and we have different systems for how the academic year is divided, quarters vs semesters. The cost of living is also very high in some places in America and dirt cheap elsewhere, there's also a much larger number of students and more useless students who would not have made it in a uni system with fewer institutes, fewer class seats and tighter admissions policies. Its just not the same, european education is not better than American by any measure after public schooling finishes.

[Anonymous No.11169559]

>>11169553
The reason I'm interested in this specific language paradox is because it doesn't feel discardable. Like, other paradoxes talk about the nature of some impossible situation, so they could never form to begin with. But this paradox is paradoxical in terms of whether it itself is possible or not, and even whether it itself is a paradox or not.

It may be solely mental, but isn't the existence of a paradoxical situation, even if purely abstract, interesting? Also, all mental states are products of physical, material, configurations of the brain. Thinking about it from that angle is pretty interesting too.

[Anonymous No.11169568]

Trying to do math for medication, because 1 pill doesn't reduce any pain and 2 pills causes drowsiness and nausea, so I'm looking to space out the pills based on effectiveness and half-life.

Suppose a medication has a half life of 6 hours, then I can represent that half life like so:
[math]\frac{1}{2}^{t/6}[/math]

And also suppose that medication has a linear peak effectiveness time of 2 hours:
[math]\min\{100\%,\frac{t}{2}\}[/math]

How could I combine the two functions in a way that makes sense? I can't just multiply them, because they body can't start filtering out the medication until it's in the system (underestimating). And I can't do a piece-wise function because the body will start filtering out a part before the whole is finally absorbed (overestimating). I've started looking into a series equation or volume flow rate calculus, but I'm in over my head. Any advice to steer me in the correct direction?

[Anonymous No.11169588]

>>11169568
there are programs to do recursive equations to high precision. Forward one small time step during the linear growth, subtract how much will be filtered given the current amount in your system, then continue linear growth

[Anonymous No.11169606]

whats the axiom of choice

[Anonymous No.11169650]

>>11169606
You have the cartesian product of two sets. If they both are non-empty, you can take whichever element of the first and the second, and you've got an element of the cartesian product.
For the cartesian products of finite amounts of sets the argument still works, and I don't recall if it worked for countable, but it completely collapses for the cartesian product of an uncountable amount of sets. However, it's still intuitive why we should be able to "choose" an uncountable amount of sets.
So the axiom of choice just states that cartesian products of non-empty sets are also non-empty.

[Anonymous No.11169660]

>>11169650
Whats this bit about taking whichever element of the first or second? I'm assuming thats what motivates the name axiom of "choice". Why can't you show that the cartesian product has any element of either set some other way - why does this have to rely on you the mathematician choosing an element rather than somehow denoting that an element intrinsically is also an element of the product?

[Anonymous No.11169669]

>>11169606
for any non-empty family of sets, there exists a choice function.

[Anonymous No.11169670]

>>11169660
>what's this bit about taking whichever element of the first or second
[math]X \times Y[/math]. Since [math]X, Y \neq \emptyset[/math], [math]x \in X[/math] and [math]y \in Y[/math], for some x and y.
Then [math](x, y) \in X \times Y[/math]
>Why can't you show that the cartesian product has any element of either set some other way - why does this have to rely on you the mathematician choosing an element rather than somehow denoting that an element intrinsically is also an element of the product?
Because.

[Anonymous No.11169735]

>>11169670
>Because.
Can you prove it?

[Anonymous No.11169807]

>>11169735
Yeah. Showing the cartesian product is non empty implies giving some [math](a, b) \rightarrow a[/math], which can either be done randomly ("by the definition, it contains some a" ) or not(we choose a particular element of the set, based on some rule). If it isn't done randomly, we can take [math]Y = { \emptyset} [/math] and have a map that sends any set to a canonical member [math]f: X \times Y \rightarrow a \in X[/math].
So for any cartesian product [math]\Pi_i X_i[/math] we can take the element [math]f(X_i)_i[/math] and show it's nonempty, which is the axiom of choice. But the axiom of choice just trivializes the whole situation in the first place.

[Anonymous No.11169812]

>>11169807
>it hid the keys
God damnit, I always forget Latex does that.
[math]Y = \{ \emptyset \}[/math]

[Anonymous No.11169821]

>>11169660
Choice isn't just about picking an unknown element of a set. That's what the existential instantiation [math] \exists [/math] is there for, you don't need choice for that since the definition of a non-empty set implies the existence of at least a single element, and the instantiation takes care of that. Take note of the implication: You are not just told that you can pick an element for an infinite Cartesian product, you are guaranteed that said product is non-empty as long as all of the sets aren't empty. If you already knew said product wasn't empty you could just use existential instantiation and be done with it.

The reason AC exists is pretty simple. The ZFC set theory is founded on first order logic. And in first order logic, statements with infinite quantifiers are not allowed, specifically, you can't just call infinite existential quantifiers. Which would be needed, since if you pick an arbitrary element then that's equivalent of saying "For set 1, we can pick an element, for set 2, we can also pick an element, ..." infinitely many times. And that happens for both countably infinite sets and sets of even larger cardinals. Basically AC exists to fill that gap, since it's a concept most people assume is what makes the most sense logically, but can't be implied from the other axioms.

Keep in mind also that you may not need choice to pick an element from a non-empty cartesian product, too. If all the sets have elements that can be picked without need for an existential quantifier, then you are good. That's because of the schema of specification, for example if you can prove all sets have a minimum, you can call the axiom schema of specification to choose the elements of all minima of every set, and you don't need existential instantiation because their existence is guaranteed. In fact that's a way the Well Ordering Theorem implies AC.

[Anonymous No.11169977]

>>11169807
>>11169821
So I'm pretty confused at this point but I'm gonna try to explain my thoughts. After this I'm gonna head to sleep, I've been awake about 30 hours now.

Basically, I see that its easy to show X and Y contain elements; they're defined to be nonempty. The thing is, it seems like when going from acknowledging X and Y have elements to showing that X*Y has at least one element, you need to say that X*Y is capable of containing an x and an y in its (x,y). The only way I can see to show that this capability is fulfilled is by saying an x and an y exist, which forces choice because you're selecting a specific x and y out of the element(s) of X and Y. I'm wondering if there's a way to bypass this last step or last two steps and show that the mere condition that X and Y contain elements is enough to show that X*Y also contains an element, without having to call upon an element directly thus being forced to *Choose*

[Anonymous No.11170002]

>>11169977
Yes. You don't need to choose in the first place, either. The existential quantifier does precisely that for you, without having to call any axiom. And existential instantiation (basically just giving a name to that one element you are calling so you can use it elsewhere) allows you to use that same element as a member of your ordered pair. Doing that for X and Y (so a finite amount of times) is perfectly valid, and from there you can either use the elements you called from both sets to make an element you already know from X*Y, or you can say that therefore X*Y is non-empty, then by definition just use the existential quantifier again to pick an arbitrary element, since at least one such element has to exist. AC is not needed in any step, as the existential quantifier can do the job for this finite product.

[Anonymous No.11170008]

>>11170002
But isnt calling the element an act of choice? If X has some unknown list of xi elements, and you use x as your called element, you're tethering x to one xi at random. Isn't that choice?

[Anonymous No.11170011]

Can:
[math]f(\tau)=sin(2\pi f_0 \tau)[/math]

Be the auto correlation function of a random process? explain why or why not

[Anonymous No.11170015]

>>11170011
so basically f = sin(Ax) where A is some constant? Well Idk what auto correlation functions are but sines dont look anywhere near random to me

[Anonymous No.11170024]

>>11170008
No. Choice (as in the Axiom of Choice) doesn't refer to the act of just choosing any element in any set under any circumstance. Just because you pick an element it doesn't mean that you are using AC. Choice in this context specifically refers to the non-emptyness of cartesian products, where none of the sets is empty. Maybe the name is a bit vague which doesn't help. But just picking an element from a non-empty set is what the existential quantifier [math] \exists [math] does by definition. You don't need choice for that, you don't even need any axioms since that is just a property of predicate logic.

[Anonymous No.11170027]

>>11170015
Its a statistics concept I think [math]\tau = t_2 - t_1[/math]

[Anonymous No.11170030]

>>11170024
Awesome, managed to fuck up the TeX somehow.

[Anonymous No.11170052]

>>11170024
Here's the thing. The reason I asked what the axiom of choice was is because I conflated it with the existential quantifier, and because I can't really comprehend the existential quantifier without the notion of choice or x having some sort of undefined nature. Before I realized that I suspected AC stuff, the only term my mind could come up with was "instantiation" but the implications of instantiations being possible seems really weird. Like, x is some element in X. Okay, which one is it? Either you use choice and say x is some specific arbitrary element (chosen), or x has no definite element, and the equation works the same regardless. This feels weird and ambiguous to work with, and only resolves and feels natural when I think about either fixing it with choice again - x is a "superposition" of all elements per se, and at the end of using x when you solve for an actual value, you choose and collapse into a specific element. Or, an equation for every element exists, and x refers to all of them in "parallel dimensions" - like the Everett approach to standard qm as described above

That last bit seems too good to be true, how can the mental processes related to considering possibilities have similar structure to QM. But it seems like a natural fit, so i dunno. I'm also not 100% sure that the last method doesn't require choice because I don't know if "all instantiations existing simultaneously" is an operable object. Like if x is in the set of reals, and you add 5 to x, do you had 5 to all instantiations? If you subtract x from x do you subtract each instantiations value from itself? I guess that seems to fit, I wonder if there are any holes. Is there any way to think of instantiations without viewing them as non intersecting realities, without reducing yourself back to choice?

[Anonymous No.11170054]

>>11169559
You'll want to read up on philosophy, specifically on Kant's "thing-in-itself"
https://plato.stanford.edu/entries/kant-transcendental-idealism/#ThinThemNoumTranObje
and then search for papers that attempt to formalize this. They will usually fall under the umbrella of "analytic philosophy", but that's not my bailiwick and you'd probably be better of asking /lit/ or /his/ for references.

>>11169977
Be careful, the problems with the axiom of choice in classical mathematics are different from the ones that arise when you work in constructive/intuitionistic mathematics.

Broadly speaking, in classical mathematics (ZFC set theory where the law of excluded middle is uncontroversial), the axiom of choice is unnecessary for finite collections, i.e. there is no issue with choosing an element from each component of X*Y. It's only used for infinite products X1*X2*X3*... where you can't write down an explicit expression X(i) for each and every component i.
For example, there's no need to invoke it for [math]\prod_{i=1}^\infty \{ n \in \mathbb{N}| n \text{ is a multiple of }i \}[/math] because i|n is a formula for the set Xi. But if your {Xi}_i are indexed by an uncountable set like R (or the irrational numbers, e.g. when constructing non-measurable sets) then there are "more sets than formulas available to express them", so we need to axiomatically postulate that such a choice function exists, without being able to spell out its rule explicitly using finitely many characters.

The issue you bring up (that the rule is underspecified) is more of an issue for constructivists, rather than classical (extensional) mathematicians who only care "that" the choice function exists as a set of ordered pairs, and ignore "how" the choice mechanism operates. If you're interested in that, you might try asking a constructivist about the "splitting/factoring/sectioning" of "surjections/epimorphisms".

[Anonymous No.11170055]

>>11170027
tau is the argument of a function so you get a sine graph in tau space.

[Anonymous No.11170057]

>>11170055
I know, that is not the problem I am having here, the thing is how can I show this can be the autocorrelation function of a random process

[Anonymous No.11170069]

>>11170054
How is constructive math any different than extensional math? A construction is just a proof that some object exists. Does either method of math have limitations that the other doesnt eg things that can only be proved one way?

[Anonymous No.11170073]

>>11170057
A random process can generate a sine wave, and if autocorrelation is just lag then phase shift it

[Anonymous No.11170084]

>>11170052
There's a lot of mixing up between existential and universal quantifiers going on here. Also note that some of this already goes beyond the realm of set theory, and isn't particularly related to AC or the rest of ZFC. Yes, you "choose" an element. But that "choosing" is not related to the Axiom of Choice, which is why I tried my best to avoid that term and use "pick" instead.
>Either you use choice and say x is some specific arbitrary element (chosen), or x has no definite element, and the equation works the same regardless
This is correct, the element you pick (or "choose", which again is NOT the same choice as AC) either becomes fixed (which is when you instantiate it, to use it in another predicate), or you actually refer to literally any arbitrary element, in which case what you want to call is the universal quantifier [math] \forall [/math] instead. If what you want to say or prove is that the equation hold regardless of [math] x \in X [/math], what you want to say is [math] \forall x \in X [/math], not just existentially instantiate a single element.
>x is a "superposition" of all elements per se, and at the end of using x when you solve for an actual value, you choose and collapse into a specific element
This is exactly the reason you call the universal quantifier. In fact, this is what universal instantiation is formally defined to do: your predicate holds for all elements in a set, and in specific you can make it hold for any one element x you pick. You could define an equation for all elements too, but with the universal quantifier that is not needed, and you don't need to have an individual [math] \exists [/math] for every element.

[Anonymous No.11170112]

>>11170084
So basically its use existential and have some form of choice, but not in the AC sense, or have alternate dimensions with a universal and don't worry about choice?

This is some pretty woah tier stuff. The thing that turned me off from existentials is that it doesn't feel as rigorous, like, the math isn't abstractly existing, it has to be generated instance by instance in your mind. There's no notation to show all the math going on, it relies on your intuitions and ability to see that if you can choose/pick any x, it works for every x. Universal is much more elegant, tons of definable systems all running at once, all operated on at the same time when you operate on x. I'm not sure if the existential qualifier is even a rigorous concept, since the symbols can't describe the thing you view in your mind, just provide you instructions on how to construct it. Maybe if the existential provided a construction that matched what you do mentally, but the mental construction seems to rely on intuitions about infinite sets that would be very difficult to rigorously prove, but I dare not say impossible because it seems like impossibility is kind of rare when it comes to basic intuitions.

Sorry if I'm talking too loosely with terms, I'm sleep deprived as fuck, but I hope we are on the same page. Also thanks for explaining it, this had been bugging me for a while. I'd read a proof, it'd hinge on existential qualifiers, and my brain would run loops for hours trying to parse it until I went - aha, instantiation!, then feel iffy about the concept of instantiation but be too confused/tired to analyze it... and repeat the next time.

[Anonymous No.11170118]

>>11170069
>A construction is just a proof that some object exists
No, a construction does more than just show that an object exists. You also want to be able to show what that object is explicitly, something AC is notoriously bad at. E.g. the Axiom of Choice guarantees that an unmeasurable set in [math] \mathbb{R} [/math] exists. In fact we can come close to actually contructing it, through the Vitali set. But then we just end up with an infinite amount of equivalence classes, and an actual Vitali set comes from using AC on those classes, but we aren't able to build the set past that. We just know it exists, and that's about it. Same with the Well Ordering Theorem, AC guarantees that every set has a total order (basically one where every single subset has a minimum, and all elements are related), including [math] \mathbb{R} [/math]. But once again, we have no clue what such an order would even look like, we just know it exists. AC is just entirely about the existence, and not about actual, explicit constructions. If you wanted to go the constructive route, a lot of these outright just couldn't be proved.

[Anonymous No.11170131]

>>11170118
This post taught me that I have got lots to learn. It just feels so trippy that chimpanzees are wiggling arcane symbols using methods that led them to realize space is curvy

[Anonymous No.11170152]

>>11170112
Yeah, more or less. Universal quantifiers allow you to work with any given element without a need to pick any one in particular. I feel there is still a bit of a misconception about existential quantifiers though. You don't really get to choose which quantifier you work with all that often. Specifically:
>it relies on your intuitions and ability to see that if you can choose/pick any x, it works for every x
Makes me think you are confusing "Let [math] x \in X [/math] ..." (universal instantiation) and "[math] \exists x \in X ... [/math]", the existential quantifier. In both of them you pick an element to work with in particular, but they are still different. The first one is the concept you wanted to get to earlier: you call a placeholder object that will be used in a following predicate, and of course you can't use any specific properties (because it doesn't have any, it's and arbitrary instance) that aren't defining properties of its containing set X. The latter allows you to pick an element, but you don't actually intend to generalize what happens to that object to every other element of X. In most cases you use it not to show anything about the set X or even the element x, but about a separate object with a property that depends on the existence of such an element x, regardless of what happens to the rest of elements in X.

Instantiation in general usually requires a materialization (or an instance, hence the name) of the set/object/whatever you are working with. That's beyond which type of quantifier you use, which instead depends on what you need it for.

[Anonymous No.11170162]

I think I'm very close on this.
We fix n = N. Then there exists [math]x_N[/math] s.t. [math]|f_N(x_N)| \geq \epsilon [/math], for sake of contradiction.

Since it's continuous at x_N, we see that [math] |t-x_N| < \delta \rightarrow |f_N(t)-f_N(x_N)| < \epsilon [/math]

And since it's decreasing, we see that [math] f_N(t) \leq |f_N(t)-f_N(x_N)| + |f_N(x_N)| < 2\epsilon [/math]

Not sure how to proceed or if I'm correct here. Any tips?

[Anonymous No.11170174]

>>11170152
Oh okay. Yeah, everything I was talking about was different ways to interpret universal instantiation then, what does the placeholder refer to, how and when does it materialize, and can the materialization event be avoided by assuming all possible instances exist simultaneously or it had a hidden preselected meaning that was set to materialize beforehand already, or a preselected meaning that referred to an unknowable element. Basically I wanted to find a sensible way to think of x (subset) X, because I think that the way its parsed in the mind and the written symbols are disconnected, or can be.

As for there exists an x in X, its just, for some such property, there exists at least one x that has that property. Thats really not at all like "for x in X"
because one is making a claim and the other is doing something akin to setting a domain, at least if interpreted sensibly

Did i get it right?

[Anonymous No.11170185]

>>11170131
>. It just feels so trippy that chimpanzees are wiggling arcane symbols using methods that led them to realize space is curvy
Mathematics and theory is really neat, but never ever forget that we only ever truly learn about Nature by toying with and poking at it.
Symbolic manipulation is cute and powerful but it doesn't mean SHIT in comparison to expirement.

[Anonymous No.11170198]

>>11170174
Outside of the formalities that seems better. Only thing I'd change is that an element x called with an existential quantifier doesn't need to have a particular property itself (unless you count "belongs in a set X" as a property), unless you use the axiom of specification to find a non-empty subset that meets a certain property. But yes, the gist of it is otherwise right: The universal instantiation gives you a particular case that must be able to be substituted by any other element of the set X (hence "universal"), and is usually used to generalize properties from that placeholder into every element. And if a property is already known, then it must hold for any element of course. The existential quantifier (and then its instantiation) gives you an element and that's about it, what you do with that element doesn't have to happen to every other element in the same set, and is usually used for a construction (or just to prove existence, like with AC) of a separate object, instead of trying to generalize a concept to the whole set.

[Anonymous No.11170229]

>>11170198
>unless you count "belongs in a set X" as a property
Not that anon, but I find it somewhat disingenuous to doubt that "x belongs to set X" is a property, given that properties (or more precisely, predicates) are and have been the standard interpretation of sets in material set theory (refer to the historical development of set theory starting with Cantor and Russell, or NBG set theory for a modern concrete example).

In other words, "x is white" is formalized by "x is an element of the set W of white things" (ignoring size issues here, so think of 'set' as an abbreviation for 'class' or 'not-necessarily-small set'). Equivalently, to the extent that properties exist, they'd be instantiated by the set of elements satisfying that property (in other words, the extension of that property).

[Anonymous No.11170256]

how can I develop some intuition regarding multivariate analysis

[Anonymous No.11170257]

>>11170256
learn some emag or fluids

[Anonymous No.11170259]

>>11170257
emag?

[Anonymous No.11170264]

>>11170259
electromagnetism
Like, learn the literal definitions of divergence and greens theorem and curl and shit but then also learn Maxwell's equations qualitatively. If you can do that, you will have more intuition.

[Anonymous No.11170435]

>>11170256
Learn about differential forms. It'll take some time, but the average mathematician just sees most of the multivariate theorems as special cases of Stokes, and Stokes is somehow easy to understand.
>>11170257
Also works.
>>11170162
Are you trying to use uniform continuity to bound the function, partition it up, and then choose n that works for some finite amount of representative elements? I think that strategy worked.

[Anonymous No.11170677]

>>11169187
Not having any traits is called emptiness in Buddhism. It's a trait that all things have. The reason you find it confusing to think of a specific object that's particularly empty of traits is because all things are empty of traits.
In logic, generally, whenever both P and ~P are true, they can be combined to make any other logical statement true. So a logician would say that the moment you encounter a paradox, the logical framework you were working with needs revision because it cannot lead to useful results because any actionable conclusion you reach will not exclude its opposite. That is to say, you will have no reason to choose one path or another because the other path will have the same reasons behind it as the first path does.
This is why people on /sci/ look askance at paradigms which expect you to deal in paradoxes. But there are communities of very intelligent and good people which work with them all the time. The Buddhists would say that a thorough understanding of emptiness leads to correct action in the given situation because compassion arises from a corollary of emptiness called dependent origination: if no object or person has qualities, nothing is self-existent or self-causing, so everything is held together only by everything else, without foundations. In that case, you can act with the recognition that all beings, things and events are nothing without each other.
You can see how the types of thinking I have characterised are very different. The logical way draws a plan as to what to do in each situation, and takes the facts of the matter and their logical relationships into account so as to know what different possibilities look like, and acts to achieve the best end. The other takes certain universal truths (or, the 'dharma') and embeds them deeply into one's way of being, thinking and doing through meditation so when a situation arises, one will act in harmony with the nature of the world.

[Anonymous No.11170680]

>>11169251
Nagarjuna gave this account of emptiness:
Things are not existent nor non-existent, nor are they both existent and non-existent, nor are they neither existent nor non-existent.

[Anonymous No.11170695]

>>11169650
>I don't recall if it works for countable
https://en.m.wikipedia.org/wiki/Axiom_of_countable_choice

[Anonymous No.11170820]

>>11170185
If I discover something in an experiment, I can show you how the experiment works and you can run it yourself and then find what I found.
If I discover something in mathematics, I can show you how the proof works and you can run it yourself and find what I found.
Is the main difference in your mind that the former has results which appear to the senses, and the latter results which appear to the mind?

[Anonymous No.11170828]

>>11170229
Whether it's a property or not doesn't have a bearing on the argument.
But my intuition is such that 'belonging to a set' and 'having a property' are equivalent

[Anonymous No.11170859]

>>11170820
Mathematics is completely different from science, epistomologically speaking. The anon I responded to seemed to suggest that we leaned spacetime is curved by doing math, but this absolutely isn't true. Science is not science without empiricism while math is explicitly a study of a priori relationships.
Experiments are not like mathematical proofs. Experimental data is king in science, it doesn't matter what your theory says if it runs contradictory to the data.

[Anonymous No.11170882]

>>11165486
I really, really want you to scan and upload this. Please~?
>>11166523
hows this

[Anonymous No.11170965]

Anyone has that calculator?

Is it possible to calculate a taylor series with more than one variables with it?

Basically i want to linearize differential equations

[Anonymous No.11171195]

guys.... how does it go from +7 to -5
.

[Anonymous No.11171202]

>>11171195
x = u - 2, so what is 6x in terms of u? then what is 6x + 7 in terms of u?

[Anonymous No.11171224]

>>11171202
oh wow
im didn't know there was that step.. thank you

[Anonymous No.11171404]

Hello guys, stupid question here. Let's say I have a set with with three total elements as members. Each element can have two possible options being A or B. There's equal 50/50 percent likely hood an element will be set as A or B. So there's a total of 9 possible sets because 3^2. How do I find the probability(%) of each possible out come, as in: what are the chances I'll get {AAB},{ABA}, {BBA}, ect... Is it 11% each time? Sorry I'm a tard....

[Anonymous No.11171494]

Any tips for a freshman at uni ?
sage cause I don't wanna bump pornography

[Anonymous No.11171622]

When irradiated with light of wavelength 471.7 nm, the chlorine molecule dissociates into chlorine atoms. One Cl atom is formed in its ground electronic state while the other is in an excited state that is 10.5 kJ/mol above the ground state. What is the bond enthalpy of the Cl2 molecule? Cl2 + 471.7 nm wavelength light ---> Cl(ground state) + Cl(excited state, 10.5 kJ/mol above ground state)

[Anonymous No.11171633]

>>11171404
>So there's a total of 9 possible sets because 3^2
no there's a total of 8 possible sets because 2^3

so it's 12.5%

[Anonymous No.11171680]

>>11171622
Cl-Cl: 242 kJ/mol per https://en.wikipedia.org/wiki/Bond-dissociation_energy.. wavelength in m=(planks contant*speed of light)/energy in J: wavelength=(hc)/E. 471.7e-9=(6.63e-34*3e8)/E; 471.7e-9=1.989e-25/E; 471.7e-9*E=1.989e-25; E=4.2166631e-19 J/atom. E*6.022e23=253927.451882 J/mol = 253.92745188 kJ/mol. 253.9274519-10.5=243.4274519 kJ/mol.

[Anonymous No.11171701]

is it a bad idea to read into /x/ shit like magic and the supernatural if i tend to believe a lot of what i read?
even if it's not real, i suspect i might incorporate the bits that seem useful or interesting into my worldview or use them in mental models. i'm tempted to do it because i think it might add some interesting flavor to my writing, but at the same time it seems like an infohazard.

[Anonymous No.11171807]

>applying for undergrad research
>"In 4-6 sentences, please describe your goals and reasons you are interested in participating in undergraduate research."
W-WHAT DO I PUT, BROS?!

[Anonymous No.11171924]

>>11159921
Scientifically speaking, which brand of diapers are best for Remi?

[Anonymous No.11171935]

>>11170256
multi-dimensional analysis:

Munkres, Duistermaat and Kolk, Spivak, Loomis and Sternberg, Zorich volume II
>>11170859
You're so dumb lol

[Anonymous No.11171938]

how can I increase my iq?

[Anonymous No.11171981]

>>11171935
i know but why

[Anonymous No.11171996]

>>11166523
Have some more.
>>11171807
"Kahler Geometry gets fifty liters of blood pumping at light speed through my half a meter dick. Please give me money so I can join up with great comrades in the open seas and we can use our raging erections to row the titanic ship of complex geometry towards the future, guided by the shining stars of the past."
Just switch kahler geometry and complex geometry for the appropriate terms in your case.
>>11171924
Fuck off.
>>11171938
Do a bunch of IQ tests.

[Anonymous No.11172067]

How much math do I need to know to post with the big boys in /mg/?

[Anonymous No.11172102]

>>11171404
the base should be how many elements you're choosing between, the exponent is how many slots you need to fill. Look up the multiplication counting principle.

[Anonymous No.11172109]

>>11172067
Know all the stuff in high school and freshman and you have my official permission to post there.

[Anonymous No.11172369]

>>11161849
I'm right here

>169cm
>doesn't go outside
>majoring physics

[Anonymous No.11172372]

>>11172109
Isn't that literally freshman math (for math majors) though?

[Anonymous No.11172392]

>>11172372
No, that's roughly a bachelor's degree at a good university.

[Anonymous No.11172575]

How do eigenvalues and eigenvectors change when a change of basis is applied? More specifically, if I were able to change a matrix into a Markov matrix through a change of basis, how would that affect the eigenvectors? Merci

[Anonymous No.11172576]

>>11172575
The eigenvalues don't change
The eigenvectors change covariantly

[Anonymous No.11172594]

if scientists are so smart then why are so many of them leftist or left biased?? is it because they are grant chasers and were bread in acadamia instead of industry???

remember when lawrence krauss defended SJWs and shillary then he was Metooed and connected to epstein?? same with tyson LOL btfo

seething boomer rage:
https://motls.blogspot.com/2016/06/leonard-susskind-vs-donald-trump.html

[Anonymous No.11172607]

Can anyone explain to me exactly how drug tests work? Does a (very) feint line present negative? I've got an employment test soon, and I've been pretty worried. Haven't smoked in several weeks, plenty of exercise and water, the normal bits. Pic related is was a cheap home test from Walmart, but everything I read online is pretty contradictory on what it means.

[Anonymous No.11172609]

Why are avocados so weird and oily?

What kind of fucking berry is tshis?

[Anonymous No.11172610]

>>11172607
I should add that in the photo, it's harder to see the pink than in person, as the strip was foggy, and hard to get my camera to focus on.

[Anonymous No.11172685]

>>11159921
What happens when you inseminate a non queen bee?

[Anonymous No.11172771]

What software is used to make graphs like these?

[Anonymous No.11172775]

>>11172771
Looks like base R.

[Anonymous No.11172815]

>>11159921
In the proper definition of a limit, why does it say |f(x) - L| < epsilon only when epsilon > 0. That would mean that f(x) could equal 0 right? I thought it couldn't.

[Anonymous No.11172838]

>>11159921
please give me a book about highschool physics

[Anonymous No.11172843]

>>11172838
forget it, i found it

[Anonymous No.11172844]

Are brain games scientifically proven?

[Anonymous No.11172885]

>>11172815
what? Of course it could be zero

[Anonymous No.11172892]

>>11172609
Seed dispersal

[Anonymous No.11173242]

I can't quite wrap my head around the notion that we are gravitationally bound to something as distant as the center of the galaxy and that the entire galaxy is moving as one unit

[Anonymous No.11173378]

I think I understand most until the last bullet point where I get confused. Why does it follow that U^2 _1 is as showed?

any help is greatly appreciated.

[Anonymous No.11173380]

Anon, quick! The situation is desperate!
For two complex numbers (a, b) and (c, d), we need you to write out (a, b)/(c, d)!
>>11172685
I don't think you can.
>>11172815
>only when
*For any epsilon > 0.
>>11172844
No.
>>11173242
Is that a question?

[Anonymous No.11173393]

>>11173380
(a, b)=(R1)exp(T1)
(c, d)=(R2)exp(T2)

(a, b)/(c, d)=(R1/R2)exp(T1-T2)
where R=sqrt(a^2+b^2) and T=arctan(b/a)

[Anonymous No.11173396]

>>11173393
whoops, forgot the imaginary unit in the arguments of the exponents

[Anonymous No.11173400]

>>11173393
Heh, nice save, but I want the real formula.

[Anonymous No.11173405]

>>11173400
that is the real formula. you can convert to rectangular form if you like.

[Anonymous No.11173408]

>>11173400
Ah, nevermind, it's in wikipedia.
>>11173405
Yeah, but I recalled there was one that did it directly, I've just never seen it used for anything.

[Anonymous No.11173409]

A quick check to see I haven't misunderstood anything. If we have some (suitably sided) modules [math]M, N[/math] over a ring [math]R[/math], and we know that [math]M\otimes_R N = 0[/math], can we conclude [math]\text{Tor}_n^R (M, N) = 0[/math] for all [math]n>0[/math]?

[Anonymous No.11173441]

I WANT TO HELP BUT WHY DON'T YOU MTFK ASK SOMETHING THAT I KNOW? FUCK.

[Anonymous No.11173448]

>>11173441
ANON WHAT IS IT THAT YOU KNOW?

[Anonymous No.11173451]

>>11173380
nigger I cant be bothered to to do [math] \frac{a+bi}{c+di} \frac{c-di}{c-di} = \frac{(ac-bd)+(ad+bc)i}{c^2+d^2} [/math]

[Anonymous No.11173483]

>>11173409
I've struggled with this for fifteen minutes before giving up, but I think you can prove it using the tor-hom adjunction and half an hour of diagram chasing.
That might also be completely hopeless and the theorem is false. It's probably false, to be entirely honest. Solid 90% chance of being false.

[Anonymous No.11173545]

>>11173483
That's what I believe, as well. At least I hope so.

[Anonymous No.11173559]

>>11172885
but why? I thought nothing could reach the limit?

[Anonymous No.11173576]

What is Swyer Syndrome exactly? From what I understand these are the closest to actual hermaphrodites that we can get, as they bear an XY genome.
I want to know exactly how it was determined that people suffering from this are somehow "female". Do these people actually have wombs, or are they completely physiologically an undeveloped man? What are they actually? Pic related is Jeanne Nollman, and to me she looks like a man in drag.

[Anonymous No.11173619]

Can one skip straight to QM if one has the mathematical background required? I don't really want to start at the bottom.

[Anonymous No.11173643]

>>11173619
No you first have to know how a seesaw works.

[Anonymous No.11173662]

>>11173559
In the domain.
The image can be whatever the hell it wants to be, it could be zero, it could be a constant, doesn't matter as long as its distance to the limit is below epsilon.

[Anonymous No.11173667]

>>11173405
based doxy poster

[Anonymous No.11173672]

What does it mean if I'm using gaussian elimination and when I try to eliminate unknowns the whole equation becomes 0 instead of just eliminating one variable, and I can't seem to frame any of the equations in a way where I can eliminate one variable at a time.

[Anonymous No.11173706]

>>11173672
If one of the rows in the augmented matrix is just a bunch of 0s but both the coefficient and the augmented matrices have the same rank then it means you have infinite solutions. Basically if one of the equations gets reduced to zero you can still keep solving for solutions as usual, but you'll get an infinite family of them that depend on a variable instead of a single one

[Anonymous No.11173719]

>>11173706
Thanks anon, I'll look up some examples. So far I can only find examples of gaussian elimination with one solution, and the problem i'm looking at clearly has infinite solutions so I'm at a loss of how to continue

[Anonymous No.11173772]

>>11173643
noooooooo

[Anonymous No.11173793]

how do i start this problem?

[Anonymous No.11173808]

>>11173619
Sure, just get some book with "Quantum Mechanics for Mathematicians" in the title. You'll need to memorize the essentials of hamiltonian mechanics and Legendre transformations with extremely poor appendix-tier intuition, and your understanding of the subject will be mathematical and not physical, but it should be doable.
>>11173793
What the fuck is a lateral deflection?
Is this some basic question about directional derivatives that I just can't read?

[Anonymous No.11173821]

>>11173793
grad w = (0, 0)

[Anonymous No.11173854]

>>11173719
Well I've been at this for a bit now and looked at several examples but I can't make my answers match the key.
Heres my system of equations
2x+3y-6z=3
-4x-6y+12z=-6
x+2y+5z=30

I know its a dependent system. I've tried solving for different variables and my answers are not anywhere close to what the key is saying it is. Any hints for how to set this thing up?

[Anonymous No.11173916]

I read an article about some genius kid from Belgium. I don't really buy into the whole thing, but is he ever a subject here on this board?
People contemplating whether it is a scam, and assuming it isn't, how one person can supposedly learn so much so quickly while being so underdeveloped?

[Anonymous No.11173945]

>>11173916
Jacob Barnett?
Yeah, sometimes. He discovered the Barnett integrable functions.
>how can one person learn so much while being so underdeveloped
By studying hard.

[Anonymous No.11174050]

>>11173854
Row operations should reduce the system to:
1 0 -27 | -84
0 1 16 | 57
0 0 0 | 0
=> x-27z=-84, y+16z=57

[Anonymous No.11174069]

>>11173854
Im not sure if I really understand your question, but Eqn 2 is clearly a multiple of Eqn 1 and so you have a singular system of equations. Using equations (1 or 2) and 3 you can write x and y in terms of z, x and z in terms of y, or y and z in terms of x. You cannot solve for all three.

[Anonymous No.11174177]

>>11173854
>>11174050
Thanks boys I figured it out. I got your answer.

[Anonymous No.11174184]

>>11174069
Sorry, I didn't give a very clear explanation. I was trying to find where three planes intersected.

[Anonymous No.11174302]

pls help i don't understand nothing

[Anonymous No.11174330]

Does anyone here have the premium version of Mathway? I'm just wondering if the steps they give are good enough.

[Anonymous No.11174338]

>>11174302
Do you know at least the basic definition of a group? Cause the proof follows almost directly, most of the conditions are met just cause [math] ( \mathbb{R} , +) [/math] itself is an abelian group. If you don't know the definition of a group then I don't know how you are attempting to solve that, and you should read up on the basics first.

[Anonymous No.11174343]

>>11174302
Just show G satisfies the following
1) closed: any z=x*y is in G
2) associativity: (x*y)*z=x*(y*z)
3) has an identity element: there exists an E in G such that x*E=x
4) inveritibitliy: for any x in G there is an x' so that x*x'=E
5) commutativity (this makes it abelian): x*y=y*z

Hint: all of these can be proven trivially since R itself is a field

[Anonymous No.11174379]

>>11174338
>>11174343
You can also just write down "every vector space is trivially an abelian group".

[Anonymous No.11174389]

>>11174338
>>11174343
thanks