/mg/ math general: Collatz Edition

[Anonymous No.9223313]

What are you studying today, /mg/?

https://en.wikipedia.org/wiki/Collatz_conjecture

Previous thread >>9209451

[Anonymous No.9223320]

>>9223313
i cant imagine being this autistic desu
i thank the gods every day

[Anonymous No.9224625]

>page 10
wtf
bump

[Anonymous No.9224773]

How do you proof -a = (-1) * a ?

[Anonymous No.9224781]

>>9224773
durham lmao?

0=0*a=(1-1)*a=1*a+(-1)*a=a+(-1)*a => -a=(-1)*a

[Anonymous No.9224783]

>>9224781
derp

[Anonymous No.9224792]

>>9223313
u have fuccin autism

[Anonymous No.9224808]

>>9223313

Bet none of you can solve this:

You start off n steps up an infinitely tall mountain. At every time-point you can move one step up or down on the mountain. However, you are constrained such that if at time-point 'x' you are at height 'y', then the next 'y' moves that you make from that point forward can never be repeated again. E.g. if you are at height 3, and then go up, up, down, it means you can never repeat that combination of three steps. Is there an upper limit on how long you can keep making moves without either violating the rule against repeating steps or arriving at the base of the mountain?

[Anonymous No.9224931]

>>9223313
QUICK I JUST REALIZED A QUESTION I CAN'T ANSWER:

What is the set of all axioms?

[Anonymous No.9224934]

>>9224931
{A | A is an axiom}

[Anonymous No.9224937]

>>9224931
Cannot be formed in ZFC

[Anonymous No.9224938]

>>9224934
No, I mean what IS it? Like what are its properties? What is its cardinality?

[Anonymous No.9224940]

>>9224937
What? How could that be? What about The set of all axioms that are consistent with ZFC

[Anonymous No.9224941]

>>9224938
about 8 or 9

[Anonymous No.9224942]

>>9224931
>What is the set of all axioms?
It's a category, not a set.

[Anonymous No.9224946]

>>9224941
No, those are the axioms of ZFC. I mean all the axiom. And I think that what I am trying to get here is:

What are the properties that an axiom should suffice? What should be in the set of all axioms?

[Anonymous No.9224947]

>>9224942
What the fuck is a category man. Tell me I need to know. And tell me about the category of all axioms

[Anonymous No.9224950]

>>9224940
I highly doubt that the axiom scheme of comprehesion would allow it, as I cannot think of a set that the set of all axioms could reside in.

[Anonymous No.9224952]

>>9224946
>>9224947
What's the mathematical equivalence of forgiveness? Allow for 'time to process'?

[Anonymous No.9224954]

>>9224950
But that doesn't make sense. We can talk about natural numbers because there is a set of natural numbers. Where do axioms come from? How can I say "Let A be an axiom". Where does that "A" come from? Where are axioms?

[Anonymous No.9224955]

>>9224947
>What the fuck is a category man.
https://en.wikipedia.org/wiki/Category_(mathematics)

I'm not a "man".

[Anonymous No.9224958]

>>9224954
The naturals can be formed in ZFC due to the empty set axiom(look at von neumann construction of naturals). To ask what is an axiom is much more of a philosophical question than a mathematical question.

[Anonymous No.9224967]

>>9224955
Are you from the set of all girls (male)?
Also that wikipedia article says nothing about axioms! It is all just a bunch of arrows I am talking about real math not little kid games. Where do axioms come from?

>To ask what is an axiom is much more of a philosophical question than a mathematical question.
That is wrong because in philosophy you can't know nothing.

If Godel proved a theorem that holds with all axioms then that means he at some point had to say "Let A be an axiom". When he uttered those words. where did A come from? If axioms do not belong in a set then how could someone prove something about all axioms?

[Anonymous No.9224972]

>14,88

[Anonymous No.9224977]

>>9224967
You are referring to Incompleteness Theorem, which is where Godel bitched about 'symbol shunting' instead of actual mathematics.

[Anonymous No.9224981]

>>9224977
What does that MEAN?

[Anonymous No.9224982]

>>9224967
Are you from the set of all Hands(Left)?

[Anonymous No.9224983]

>>9224981
Are you from the set of all Hands(Right)?

Or are you Hand-ed(Left|Right)?

-ed = suffix

[Anonymous No.9224984]

>>9224982
No I am not a hand but I am left-handed

[Anonymous No.9224987]

>>9224984
1<0
0>1
0!1
0|1
Left|Right
Female|Male
Color|Blue
Hot|Cold
Up|Down

[Anonymous No.9225123]

>>9223313
Time series econometrics.

There are like zero online resources for this shit and my textbook isn't helpful at all. Muddling through though

[Anonymous No.9225161]

>>9224808
>Is there an upper limit on how long you can keep making moves without either violating the rule against repeating steps or arriving at the base of the mountain?
yes

[Anonymous No.9225213]

>>9224967
>When he uttered those words, where did A come from?
A does not exist. It's a made up object which embodies the 'ideal form' of an axiom. For example, when we say something like "Let x be a number", we are not consulting the set of all numbers, and drawing out one of our choice. We are simply considering the properties of the 'ideal form' of a number, which all numbers must be faithful to; indeed, the set of all numbers is exactly those objects which are in alignment with this ideal form.

[Anonymous No.9225234]

>>9225213
But if there is an ideal form all axioms take then why can't we just make S the set of all the objects that have those properties?

[Anonymous No.9225253]

>>9225213
define "ideal form"

[Anonymous No.9225344]

>>9224972
Anti-semitic numbers are illegal anon.

[Anonymous No.9225408]

>>9223313
What's the formal definition of infinity in abstract algebra/analysis?

[Anonymous No.9225415]

>>9225408
There is no formal definition. We call something "infinite" when it has more parts than any counting number, goes on in an endless succession of steps, is a point in an order after all counting numbers, or similar.

[Anonymous No.9225416]

>>9225408
>What's the formal definition of infinity in abstract algebra/analysis?
Depends on the context
https://en.wikipedia.org/wiki/Extended_real_number_line
https://en.wikipedia.org/wiki/Riemann_sphere

[Anonymous No.9225736]

>>9225408
Nu professor said that a set is infinite if every subset of it is a bijection with the entire set.

[Anonymous No.9225752]

>>9225736
no. if SOME subset of it is a bijection with the entire set. the empty set will not be in bijection with anything else and it's a subset of every set.

[Anonymous No.9225773]

[math]Show \space me \space some \space cool \space stuff \space you \space can \space do \space with \space LATEX[/math]

[Anonymous No.9225883]

>>9225773
[math](^\frown \smile ^\frown)[/math]

[Anonymous No.9225891]

>>9225773
[math][/math] ▲
▲ ▲

[Anonymous No.9225901]

>>9225773
[math] \space [/math] ▲
▲ ▲

[Anonymous No.9225907]

>>9224773
-a = -1 * a
(-a)*1 = -1*a

L:((-a)*1)/1 = -a
R:((-1)*a)/1 = -a

[Anonymous No.9225911]

>>9224808
If I'm understanding that correctly, you've essentially got an easy language you can build for this.

It goes:
for n = 1 => infinity: up*(n + 1), down*n

[Anonymous No.9225956]

>>9225911

I don't think that solution works, unfortunately, because the next time you repeat the 'down' step, the former down steps are a substring of it.

[Anonymous No.9225957]

>>9223320
you never studied the collatz conjecture? lol

[Anonymous No.9225988]

>>9224808
at height 2^n, go up 2^(n-1), down 2^(n-1), up 2^n
dunno if i understood the question 2bh

[Anonymous No.9225991]

>>9225988

Should clarify you can only move on step up or down per time-point. The problem with your solution is that at height 2^(n-1) you went down 2^(n-1) steps. So the next time you go up and down, you will be repeating those 2^(n-1) downward steps.

[Anonymous No.9226020]

>>9225991
you go down 2^(n-1) steps from height (2^n + 2^(n-1)) = 3*(2^(n-1)) down to height 2^n

[Anonymous No.9226906]

>>9225752
if some PROPER subset of it is in bijection with the entire set. [math]A\subset A[/math] always

[Anonymous No.9227347]

>>9225736
>infinite sets
No such thing.

[Anonymous No.9227586]

>>9227347
>being a zenophobe

[Anonymous No.9227825]

>>9225736
>a set is infinite if
>if
Yes, "if".

[Anonymous No.9227835]

what is 4|n denoting here?

[Anonymous No.9227838]

>>9225773
[eqn]
\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}^{\sum\limits_{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}^{\sum\limits_{\sum\limits_{}^{}}^{\sum\limits_{}^{}}}}}}
[/eqn]

[Anonymous No.9227891]

>>9227835
4 divides n

[Anonymous No.9227979]

I know that this probability function is a multivariate normal distribution in d-space. How do i next proceed in deriving the classifier? Do I have to get an expression from the sum over C1,2 or ?

[Anonymous No.9228027]

>>9225773
i like real analysis

[math]{\color{red}{\text{(USER WAS BANNED FOR THIS POST)}}}[/math]

[Anonymous No.9228184]

okay here's a problem I couldn't solve for the last hour

Given a1 + a2 + a3 ... + an = k
Where each a and k are positive integers
Describe lcm(a1, a2, a3 ... , an) in terms of k

[Anonymous No.9228205]

>>9228184
Given that n people died in a forest, describe their gender in terms of their jobs.

[Anonymous No.9228213]

>>9228205
Well the original question is just finding the maximum order of S12
I'm autistically overcomplicating things here because I don't like proof by exhaustion

[Anonymous No.9228217]

>>9228184
>Describe lcm(a1, a2, a3 ... , an) in terms of k
Be more specific, it's not clear at all what kind of answer you're expecting

[Anonymous No.9228226]

>>9228213
Is it 35?

[Anonymous No.9228230]

TURN ON CNN

Is Goldbach Conjecture true?
https://arxiv.org/pdf/1710.04081.pdf

>We answer the question positively. In fact, we believe to have proved that every even integer 2N≥3×10^6 is the sum of two odd distinct primes. Numerical calculations extend this result for 2N in the range 8−3×10^6. So, a fortiori, it is shown that every even integer 2N>2 is the sum of two primes (Goldbach conjecture). Of course, we would be grateful for comments and objections.

[Anonymous No.9228233]

>>9228217
Ugh my brain hurts and I can't write for shit
I meant find the max value of lcm(a1, a2...) for a specific k
>>9228226
No definitely not. disjoint cycles of order 3,4,5 form a order 60 permutation group in S12

[Anonymous No.9228235]

>>9228217
The maximum order of S_n, which is
max_{1 =< a1, ..., a_m integers, a1+...+a_m = n} lcm(a1, ..., a_m).

I think there's no nice formula for this, but there's probably asymptotic formulas and bounds for this. Actually I think that Landau did find and prove some asymptotic formula.

[Anonymous No.9228237]

>>9228235
>The maximum order of S_n
There's only one order for a group, what is "maximum" supposed to mean?

[Anonymous No.9228240]

>>9228237
I've meant order of elements of S_n, sorry.

[Anonymous No.9228245]

>>9228240
Then you have the upper bound of n!.

[Anonymous No.9228254]

>>9228245
And n is a lower bound. Great, we have something.

[Anonymous No.9228267]

>>9228254
>we have something.
Speak for yourself.

[Anonymous No.9228284]

>>9228245
>>9228254
>>9228267
What the fuck it actually exists

[Anonymous No.9228294]

>>9228284
Yeah, Landau, I knew it.

This doesn't seem to help for n=12 though, the exponential bound gives g(12) =< 314.

[Anonymous No.9228338]

I'm studying parsing theory, and found this definition:

A sequence of nodes [math](a_0, a_1, \dots , a_n), \mbox{ } n \geq 0[/math], is a path of length [math]n[/math] from [math]a_0[/math] to [math]a_n[/math] in a graph [math]G[/math] if for all [math]i = 0, \dots, n - 1 \mbox{, } (a_i, a_{i + 1})[/math] is an edge of [math]G[/math].

I would like you to help me: what about when [math]n = 0[/math]? But before, a bit of context: the book I'm reading defines a graph [math]G=(A,R)[/math] where [math]A[/math] is the set of nodes and [math]R[/math] is a relation on [math]A[/math]; the elements of [math]R[/math] are called the edges of [math]G[/math].

If [math]n = 0[/math] then, a path of length zero from [math]a_0[/math] to itself is a sequence whose only element is [math]a_0[/math], then, for all [math]i = 0, -1[/math], [math](a_i, a_{i + 1})[/math] is an edge of [math]G[/math]. But in this particular case, the two posible edges are [math](a_0, a_{-1})[/math] and [math](a_{-1}, a_0)[/math], but none of these is an edge (or an element of [math]R[/math]); actually, [math]a_{-1}[/math] not even exists in our given sequence. Is it possible to have a zero length path given the above definition? Is it vacuously true? why?

[Anonymous No.9228645]

>>9228338
a zero length path is just a point, no edges involved

[Anonymous No.9228738]

>>9228645
Yes, but why? I mean, that could be deduced from that definition.

[Anonymous No.9228746]

>>9228738
>Yes, but why?
because you have a node and there's no edges that don't fit the edge criteria

[Anonymous No.9228755]

>>9227835
>n^2<0 or 2 = 3

[Anonymous No.9228757]

>>9227835
0 is odd?

[Anonymous No.9228760]

>>9228230
>Odd numbers larger than 2 are prime;
>3 is prime, 5 is prime, 7 is prime, 9 is left as exercise, 11 is prime, 13 is prime...

[Anonymous No.9228782]

>>9223313
How to proof with set identities?
(A − B) − C = A − (B ∪ C)

[Anonymous No.9228806]

>>9228782
show elements are the same

[Anonymous No.9228809]

>Hartshorne

[Anonymous No.9228810]

Threadly reminder to work with physicists.

[Anonymous No.9228814]

>>9228782
[math]x \in (A\setminus B)\setminus C \Leftrightarrow (x \in A) \land (x \not\in B) \land (x \not\in C) \Leftrightarrow (x\in A)\land (x \not\in B\cup C) \Leftrightarrow x\in A\setminus (B\cup C)[/math].

[Anonymous No.9228816]

>>9228806
Is this correct?

[Anonymous No.9228818]

>>9228816
probably
I thought it was \ instead of -

[Anonymous No.9228820]

>>9228818
>tfw I'm too dumb

[Anonymous No.9228841]

>>9228818
mine is wrong. I'm confused between the set builder notation and set identities

[Anonymous No.9228850]

>>9227838
fucking hate snakes

[Anonymous No.9229041]

How to do the inner summation? (the one with 4) I will figure out the rest.

[Anonymous No.9229048]

>>9229041
that summation doesn't make sense.
are you sure you didn't exchange the two sums?

[Anonymous No.9229054]

>>9229041

$sum_{i=1}^j 20-8i$

[Anonymous No.9229085]

>>9229041
>>9229048

[Anonymous No.9229086]

>>9229048
>doesn't know about the linearity of summation

[math]\sum\limits_{a} \sum\limits_{b} f(a, b) = \sum\limits_{b} \sum\limits_{a} f(a, b)[/math]

[Anonymous No.9229087]

>>9229086
1) I don't think you know what linearity means
2) That's not true when the b's depend on the a's.
3) It does not make sense when the a's depend on the b's

[Anonymous No.9229099]

>>9229086
p. sure that won't work for some sequences if a or b tends to infinity

[Anonymous No.9229105]

>>9229086
[eqn]
\sum_{i=1}^{j} \sum_{j=1}^{4} 2(j-i)=\sum_{i=1}^{j} 20-8i
[/eqn]
[eqn]
\sum_{j=1}^{4} \sum_{i=1}^{j} 2(j-i)=\sum_{j=1}^{4}2\left (j\left [\sum_{i=1}^{j}1 \right ]-\sum_{i=1}^{j}i = \right ) =\sum_{j=1}^{4}2\left (j^2-\frac{j(j+1)}{2} \right ) = \sum_{j=1}^4 j^2-j = 20
[/eqn]

[Anonymous No.9229116]

>>9224955
Lmao. You're that tranny cunt from the constructive math thread I started, aren't you?

[Anonymous No.9229128]

>>9229041
That's

[math]\sum_{i=1}^j 2 sum_{j=1}^4 (j - i)[/math]

[math]\sum_{i=1}^j 2 (\frac{4(4+1)}{2} -4i)[/math]

[math]\sum_{i=1}^j 20-8i[/math]

[STOP HERE IF YOU WANT TO FIGURE OUT THE REST FOR YOURSELF]

[math]20j - 8 \sum_{i=1}^j i[/math]

[math]20j - 8 (\frac{j(j+1)}{2})[/math]

[math]16j - 4j^2[/math]

----
Does anyone know where I can learn to sketch implicit (or just strange) functions? For instance, I want to be able to easily sketch things like

tan(y) = x^2
x^2 - ny^2 = 1
y = ln(x)/sin(x)

and so on.

[Anonymous No.9229144]

>>9229116
>You're that tranny cunt from the constructive math thread I started, aren't you?
I'm not a "tranny cunt", and I don't know what thread you're referring to.

[Anonymous No.9229149]

>>9229144
Kill yourself you mentally ill twat

[Anonymous No.9229152]

>>9229149
>Kill yourself
Why?

>mentally ill twat
I'm quite well mentally.

[Anonymous No.9229170]

>>9229152
Because you always have to bring yourself up. Just like you did in the other thread.

[Anonymous No.9229174]

>>9229170
>Because you always have to bring yourself up. Just like you did in the other thread.
Someone else brought me up, not I.

Please learn to read before posting again.

[Anonymous No.9229178]

>>9229174
>Someone else brought me up
Wrong, "bringing up" someone means that the intended subject of the conversation is that someone. The person who did that was you, in both threads.

Please learn basic language skills before attempting to reply.

[Anonymous No.9229180]

>>9229178
>, "bringing up" someone means that the intended subject of the conversation is that someone.
see
>>9229116

[Anonymous No.9229186]

>>9229180
see, I merely participated in the conversation after you brought yourself up
>>9224955

[Anonymous No.9229195]

>>9229186
If mentioning the word 'man' is bringing myself up (depite it not, that's the whole point), then this poster brought me up: >>9224947

[Anonymous No.9229225]

>>9229195
Not understanding context isn't smart or clever. If I say "What's X, dude?" I am not bringing said dude up. Simply mentioning "man" isn't bringing anyone up as >>9224947 demonstrates. But you brought up your gender with your response (multiple times now).

[Anonymous No.9229427]

>>9229225
>If I say "What's X, dude?" I am not bringing said dude up
How are you not bringing said person up when you directly (attempt to) address them?

>But you brought up your gender with your response (multiple times now).
I brought up my sex, not my gender; I'm not sure why this is so confusing for you.

[Anonymous No.9229434]

9228810
>>>/r/dogs/

[Anonymous No.9229470]

>>9223313
Can someone tell me what second order differentiation is used for? I've been using it a lot recently foremost in its application to vectors and to determine how dampened stuff is under simple harmonic motion (at least I think it is used for that reason, no idea what I'm doing other than solving problems). What actually is the point of it though? Why do we use second order differention, what the heck even is an "order" and why is this being applied to vectors?

[Anonymous No.9229474]

>>9229470
acceleration is an important second derivative

[Anonymous No.9229489]

>>9229474
Do you mean second derivative as in you have to differentiate twice overall from displacement - velocity - accel?

[Anonymous No.9229492]

>>9229489
>Do you mean second derivative as in you have to differentiate twice overall from displacement - velocity - accel?
yes

[Anonymous No.9229505]

Is there a geometric significance to the saturation of a multiplicatively closed set?

Localization is used all the time in geometry but I have never seen saturation mentioned.

[Anonymous No.9229536]

>>9229470
curvature depends on the second derivative, torsion on the 3rd, probably higher dimension analogues depend on 4+

[Anonymous No.9229540]

can someone post the "proof: think" pic?

[Anonymous No.9229543]

>>9229492
That's all it means? And the "second order" part is the same thing? So what do call the displacement then, the base? the "0"th derivative.

>>9229536
So we're just using second order differentials to find the curvature of things - and under harmonic motion the curvature (x with the double dots) is essentially determined via acceleration that, Holy shit if this is right my mind will be fucking blown, if not it will probably be blown even more.

[Anonymous No.9229552]

>>9229505

Significance in what sense? Once you have the group of units (since they all divide 1), you can add more elements in pretty boring ways, so I'm not sure its any more interesting than a simple multiplicatively closed group.

[Anonymous No.9229558]

>>9223313
Who is /stats/ itt?

[Anonymous No.9229576]

Any tips for teaching myself higher level algebra and trig/calculus/physics? Upraising and public education really mishandled a learning disability and I tapered off in math even though I was gifted. Never got past HS algebra, but im doing good in uni and goning to be switch to astronomy soon, but im behind in my math capabilities and could use some advice.

[Anonymous No.9229585]

>>9229576
Depends on the purpose.

[Anonymous No.9229589]

>>9229576
I know everyone recommends Khan academy and the like but I personally would go with textbooks. Read everything, do as many problems as possible, have a dedicated binder or notebook. And do it in order (ie. precalc before calc).
I like textbooks, I feel like you don't even really need a lecturer if you have a good textbook.

[Anonymous No.9229594]

>>9229552
For an affine scheme [math]X = \operatorname{Spec} R[/math] the local ring is [math]{\mathcal{O}_{X,\mathfrak{p}}} = {S^{ - 1}}R[/math] for the mult. closed subset [math]S = R - \mathfrak{p}[/math].

Suppose [math]{\bar S}[/math] is the saturation of [math]S[/math]. Is there anything interesting about [math]{{\bar S}^{ - 1}}R[/math] from a geometric perspective?

[Anonymous No.9229595]

>>9229589
+1, Khan academy is piece of shit.

[Anonymous No.9229603]

>>9229585
Most likely cosmology/physics, my uni is top-tier for exo-planets research, so I think im gonna jump on the opportunity to do research and hopefully get on board with the next gen of super telescopes planned

[Anonymous No.9229606]

>>9229595

I bet the founder doesn't even know 10% of the topics anymore, and just looked them up on wikipedia/other educational sites before making the exercises/videos. I bet even most professors copy one or two other textbooks when they make theirs.

[Anonymous No.9229609]

>>9229603
Good way is to actually start studying your subject,and then learn math you need from books. You will see what exactly you need to know, thus will be able to decide which book is good for you.

[Anonymous No.9229619]

> be me
> found an inconsistency in a lecture content
> tell lecturer
> "huh duh ya I just skipped a couple of steps, it is obvious anyway, I need to go now"
I also think that I am literally the only one who noticed it.

[Anonymous No.9229623]

>>9229619

I've done TAing, and believe me the lecturers give zero fucks. Most TAs review the material one hour before the class, and most lecturers lift most of the content from online sources (sometimes embarrassingly blatantly) and then keep things the same for the next 5 years.

[Anonymous No.9229629]

>>9229623
TA?

[Anonymous No.9229637]

>>9229427
kill yourself tranny faggot

[Anonymous No.9229640]

>>9224808
I like this problem, I have homework due at midnight and then I'm going to look at it harder. My first thoughts are that your first n steps should all be up, to get away from lower numbers. Intuitively it seems you should get stuck but I'm not certain. You definitely get stuck if the starting height is too low. Im guessing you look at the average rate of ascent and that tells you how quickly forbidden sequences are being added, which is 1per step if you're not moving on average.

[Anonymous No.9229652]

How much maths do you want to learn, /mg/?

[Anonymous No.9229660]

>>9224808
>infinitely tall mountain
No such thing.
[math]\square[/math]

[Anonymous No.9229682]

>>9224955
>I'm not a "man".
Such miserable vermin shouldn't be participating in this thread.

[Anonymous No.9229702]

>>9229652
As much as I possibly can in the fields I'm interested in.

[Anonymous No.9229714]

>>9224937
Where does his post mention Z*C?

[Anonymous No.9229783]

>>9229637
>tranny
Why the transphobia?

[Anonymous No.9229833]

9229783
Subhumans aren't welcome in these threads.

[Anonymous No.9229856]

>>9229470
It can be used to approximate the function, to determine maxima and minima, help you draw the function's graph, ...

[Anonymous No.9229973]

>>9229637
>faggot
Why the homophobia?

[Anonymous No.9229988]

>>9229973
>>>/r/taiwan/

[Anonymous No.9229990]

>>9229988
What's the relevance of Taiwan?

[Anonymous No.9230011]

TURN ON CNN

https://arxiv.org/pdf/1710.04503.pdf
A solution of 3x+1 problem
We present a solution of 3x+1 problem. For a history of this problem we refer the reader to Lagarias, Jeffrey C.

Who wants to play 'be first to spot the error'?

[Anonymous No.9230019]

>>9230011
>Our proof will be on the natural induction on the number x.

[Anonymous No.9230029]

>>9223313
proof assistant.
Toying with some coq axioms. I need to figure out how to avoid inconsistencies (but I don't get what impredicativity actually is).

[Anonymous No.9230040]

I'm studying topology, and God I'm loving it, in fact I find it easier than analysis, and their not going easy on me.

Btw, analysis is boring and a pain in the ass.

[Anonymous No.9230088]

>>9230011
It would be cool if she was correct, I like small solutions. They're elegant.
Btw she's Hungarian, so bonus points for her.

[Anonymous No.9230190]

>>9227891
>>9228757
Thanks! Learning a lot of notation lately and I guess I missed some of it when skimming material.

[Anonymous No.9230269]

>>9230040
I avoided anything analytic for a long time because I thought it was boring and tedious

Just coming back around to differential geometry after doing mostly algebra stuff, and I find it much more enjoyable now (that I can use algebra to avoid the analytic bits haha). I finally kinda get cohomology, which was too abstract for me from the purely algebraic perspective, but de Rham is nice and geometric.

[Anonymous No.9230366]

I talk to around 5 females every month with a standard deviation of 2, and the chance of a random female becoming my GF is around 0.1%

Calculate the average expected time for me to get a gf.

[Anonymous No.9230381]

Official /mg/ notepad
https://etherpad.net/p/agdg

[Anonymous No.9230389]

>>9230029
The type theory behind Coq is pretty well studied, what axioms are you trying out?

[Anonymous No.9230461]

>>9230366
Let [math]T[/math] be the random variable of the number of months required to meet your gf, then we seek, [math]E(T)[/math], first note that we model [math]T \sim Geometric(p) [/math] where [math]p[/math] is the probability of meeting your gf in a single given month, independent of any of the other months.

So now we seek [math]p[/math], the number of females you meet every month can be modeled by a Poisson distribution [math]N \sim Poisson(5) [/math], although this brings the theoretical standard deviation to [math]\sqrt{5}[/math], it should be fine for the model. Now, the amount of gfs you meet in a single month can be modelled by,

[math]S = \sum_{i = 0}^N X_i [/math] where [math]X_i \sim Bernoulli(0.01) [/math] are independent and identically distributed (note this is a random sum with number of summands a random variable N). But we only care about when [math]S = 1 [/math], to find this, we use the law of total probability

[math]P(S = 1) = \sum_{n = 0}^{\infty} P(S = 1 | N = n) \cdot P(N = n) = \sum_{n = 0}^{\infty} P(S = 1 | S \sim Binom(n, 0.01)) P(N = n)[/math]

We find this to be from a bit of analysis,

[math\displaystyle ]P(S = 1) = \sum_{n =0}^{\infty} \binom{n}{1} 0.01 \cdot 0.99^{n-1} \cdot \frac{e^{-5} 5^n}{n!}= 0.0475 [/math]

Therefore we conclude [math]p = 0.0475 [/math] is good for our model of [math]T[/math], but the expected value of a geometric variable is simply [math]1/p [/math], therefore we conclude that

[math]\displaystyle E(T) = \frac{1}{0.0475} = 21.5 \ \text{months} [/math]

So you are expected to get a gf in 21.5 months

[Anonymous No.9230465]

>>9230366
>>9230461
Wait nevermind, I accidentally read 0.1% as 1%, in that means we model it using a Bernoulli(0.001) variable instead of 0.01, in that case the expected value comes to about 200 months, rip anon

[Anonymous No.9230467]

>>9230465

[Anonymous No.9230537]

Plz help a brainlet out

[Anonymous No.9230554]

Plz help a brainlet out

[Anonymous No.9230561]

>>9230366
>>9230554
>>>/sci/sqt/

[Anonymous No.9230863]

I seriously wrote "Proof: Trivial." for the first time today.

[Anonymous No.9230923]

>>9230863
Where?

[Anonymous No.9230953]

>>9230923
In my notebook of proofs.

[Anonymous No.9231087]

can anyone help me with some basic functions stuff? I'm clearly misunderstanding some very fundamental.

if f(x) = 1x2-1, find f(2x)
my solution was to simply start off replacing the x in the original equation and adding parentheses:
f(2x)=1(2x)2-1
multiplying out the brackets:
=2x2-1
Assuming I'm correct thus far, where do I go from here? I thought perhaps 2x should be multiplied by 2, giving:
f(2x)=4x-1
However, this is incorrect. What skill am I missing here? I feel like my algebra is very weak and it's holding me back.

[Anonymous No.9231423]

>>9223313
Is tensor basically a vector function?

[Anonymous No.9231432]

>>9231087

f(x) = 1x2 -1 = (1*2*x)-1 = 2x -1

So then f(2x) = 4x -1

So you are right.

[Anonymous No.9231531]

>>9230011
The induction step in Lemma 2.2 may reduce to a case not covered by the lemma.

[Anonymous No.9231564]

>>9231432
Strange. According to the practice assessment I've been sitting the answer is wrong. It's not a syntactical thing either, because it presents four possible answers, none of which are 4x-1. I suppose I'll have to email my lecturer.

[Anonymous No.9231669]

Am I losing my mind or are 11 & 12 wrong? I think theyre off by one n term

[Anonymous No.9231674]

>>9231669

[Anonymous No.9231695]

>>9231669
Are those Fibonacci numbers?

[Anonymous No.9231700]

>>9231695
Yes

[Anonymous No.9231809]

>>9231674
you probably use 10. in your working for 11 and 12

[Anonymous No.9231900]

>>9231669
>>9231674
see when I plug in n=3 I get the sixth Fibonacci number squared which is (8)^2. So the left hand side would read (1)(1)+(1)(2)+(2)(3)=9. That's three terms, so am I looking at this wrong? It is not until the (1)(1)+(1)(2)+(2)(3)+(3)(5)+(5)(8)=64 fifth term that the sum equals the sixth Fibonacci number squared.

[Anonymous No.9231912]

>>9231900
nvm. Im an idiot

[Anonymous No.9232716]

>page 8
ffs

[Anonymous No.9232769]

I have this ugly equation. Im talking worse than
y=x^2+x^9+xcos^2(pi/17). And I need to solve for x.
How feasible is this.
Technically I need a computer to be able to do this, but only for 256 values of x. So Im considering hashing it if solving for x in terms of y is not reasonable.

[Anonymous No.9232781]

>>9232769
see >>9230561

[Anonymous No.9232784]

I have this ugly equation. Im talking worse than
y=x^2+x^9+xcos^2(pi/17). And I need to solve for x.
How feasible is this.
Technically I need an embedded chip to be able to do this in real time, but only for 256 values of x. So Im considering hashing it if solving for x in terms of y is not reasonable.

[Anonymous No.9232785]

>>9232784
see >>9232784

[Anonymous No.9232789]

>>9232785
?

[Anonymous No.9233062]

>>9232789
Ask in >>>/sci/sqt/

[Anonymous No.9233122]

>>9232784
are you looking for an inverse function?
this might not exist in most cases though.
If you're just looking for an x corresponding to a particular y value, you can use newton's method
https://en.wikipedia.org/wiki/Newton%27s_method
or if it's a polynomial you can use numerical linear algebra to find it's roots
https://en.wikipedia.org/wiki/Companion_matrix
https://en.wikipedia.org/wiki/QR_algorithm

[Anonymous No.9233200]

>>9223313
Why 3n+1 and not something else?

[Anonymous No.9233211]

>>9233200
when you change to an+b some values of a or b are known to have numbers which don't eventually go to 1 (not 100% sure but I think even 5n+1 doesn't work)

[Anonymous No.9233218]

>>9233211
Thanks

[Anonymous No.9233387]

>>9225957
only gay people show interest in Collatz conjecture.
Chads do stat&prob

[Anonymous No.9233421]

Hello /mg/
I'm pretty buttblasted at this linear algebra course
I need retarded-level material to learn
pls help

[Anonymous No.9233426]

>>9233421

[Anonymous No.9233533]

What's the difference between calculus and analysis? We don't use the term calculus where I live and it always confuses me when people here talk about calculus/analysis courses.

Is calculus just "applied analysis", as in, you just learn how to use integrals/differentiation as a tool, without necessarily understanding the actual theory behind it?

[Anonymous No.9233542]

>>9224808
Gosh I've puzzled over this one for a while and I haven't been able to figure it out. I know you're bounded for n = 2 and 3. I believe it's bounded for n = 4. 5 I don't know and beyond that I don't think it's bounded. I've tried generating solutions with a few heuristics and it seems to explode over 5. I can get sequences several thousand long for n = 5.

[Anonymous No.9233564]

>>9233542
I’m not understanding the question. Can you show your working for 2,3,and 5?

[Anonymous No.9233594]

>>9233542

I am the one you (You)'d. Here's an easier version of it that no one on /sci/ has been able to crack either.

If we have, for a fixed constant n:

[math]x_j \in \{0,1\}[/math]

[math]x_0 = 1[/math]

[math]s_i = n + \sum_{j=0}^{i} x_j [/math]

is there any infinite sequence of [math]x_i[/math] such that for any integers [math] 0 \leq i \leq \infty [/math] and [math] 1 \leq t \leq \infty [/math] we have:

[math]\{x_i,\cdots,x_{s_i}\} \neq \{x_{i+t},\cdots,x_{s_i + t}\}[/math]?

Its the same puzzle, but instead of bounding the number of steps by the height on the mountain, you bound them by the number of 'up' moves that have occurred by time T, plus a starting constant n.

[Anonymous No.9233598]

I've been looking for the "plane seats" riddle. Anyone know it? It goes something like this...

An empty plane has N seats. Each passenger has an assigned seat. They board the plane one at a time. The first passenger sits in a random seat. The next passenger does the same... but eventually someone will have to move to their actual assigned seat... can't remember the rest.

[Anonymous No.9233602]

>>9233598
https://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1349474580

[Anonymous No.9233639]

>>9229470
The Laplace operator [math]\Delta = d\delta +
\delta d[/math] on a manifold [math]M[/math] is fundamental.
First of all by Hodge decomposition all de Rham cohomology groups are characterized by harmonic forms [math]\omega[/math] where [math]\Delta \omega = 0[/math]. This fact leads to the fact that the analytic index of [math]\Delta[/math] is the second Betti number of [math]M[/math]. This is one of the first indications of the Atiyah-Singer index theorem, which is true for all elliptic operators (i.e. operators that are at most degree 2 polynomials on the Fourier side).
Second of all the harmonic forms [math]\omega[/math] minimizes the energy functional [math]E:\Omega^{(n-1)/2}(M) \rightarrow \mathbb{R},~E[\alpha] = \int_M |d\alpha|^2[/math] where the norm is defined in terms of the Hodge dual [math]\ast[/math]. This is one of the first indications of topological field theories where the minimization of the action is purely classified by topological data. These minimal configurations are usually called instantons.
Third of all (and perhaps the most important point) is that second-order differentials in the equations of motion show up as first-order differentials in the action of your theory, and in general a first order expansion in an effective field theory gets you those kinds of terms in the action due to some symmetry considerations. In addition these kinds of terms behave very nicely under second quantization so quantum field theories with these terms are well studied.

[Anonymous No.9233643]

>>9233639
faggot

[Anonymous No.9233645]

>>9223313
Nice, you took my advice.

[Anonymous No.9233659]

>>9233643
>faggot
Why the homophobia?

[Anonymous No.9233662]

>>9233645
>Nice, you took my advice.
What advice?

[Anonymous No.9233671]

>>9233659
because you are being a faggot

[Anonymous No.9233677]

>>9233671
>faggot
Why the homophobia?

[Anonymous No.9233696]

ok my (undergrad) thesis adviser just told me that I need to know approximately what fiber and vector bundles are, some examples, and operations on them like whitney sum.

I know very little algebraic topology, namely just a bit about the fundamental group and simplices.

Wat do? Good books that get me up to speed this fast?

[Anonymous No.9233733]

>>9233696
What book depends on the context. Are you studying algebraic/differential topology/geometry?

[Anonymous No.9233734]

>>9233677
because you are being a faggot

[Anonymous No.9233756]

>>9233733
algebraic topology

[Anonymous No.9233759]

>>9233677
Because faggots are subhuman.

[Anonymous No.9233823]

>>9233756
Then you should probably just get Hatcher and read the relevant sections.

[Anonymous No.9233947]

>>9233533
>calculus and analysis

[Anonymous No.9233969]

>>9233533
There's no difference. Calculus is Analysis.

[Anonymous No.9234450]

I don't understand.

Equation
a = 5
has a geometric shape of a point (0-dimensional solution set)

Equation
a + b = 5
has a geometric shape of a line (1-dimensional)

Equation
a + b + c = 5
has a geometric shape of a plane (2-dim)

Does
a + b + c + d = 5
have geometric shape of a 3-space?

Does equations of this form always have a solution set whose dimension is the number of free variables in the equation? Assuming all variables are nonzero

[Anonymous No.9234462]

>>9234450
it can be used to describe a 3d object in 4d space if thats what you are asking

[Anonymous No.9234487]

>>9234450
You got it backwards, it depends on the ambient space you work with. For example we represent the plane as [math]\mathbb{R}^2[/math], that is as pairs of numbers with coordinates denoted by [math](x,y)[/math]. For a three-dimensional space you add the [math]z[/math]-coordinate. So our model of space is [math]\mathbb{R}^3[/math], those are triples of numbers, denoted [math](x,y,z)[/math]. A line is just [math]\mathbb{R}[/math], there's just the [math]x[/math]-coordinate.

Now in general, adding an equation lowers the dimension by one. If you consider the equation [math]x+y = 5[/math], you probably think of it as of an equation in [math]\mathbb{R}^2[/math] and in this case the solution is 1-dimensional: it's a line. But this is also a valid equation in [math]\mathbb{R}^3[/math]. It's in the usual form [math]ax + by + cz = d[/math], it just so happens that [math]c = 0[/math]. In this case the solution is 2-dimensional, it's a plane. But notice that in both cases, the solution is 1 dimension lower than the ambient space. If you add another equation, you will get either a 1-dim object in a 3-dimensional space (a line), or a 0-dimensional object in a plane (a point).

tl;dr the formula is dimension = dimension of ambient space - number of constraints

[Anonymous No.9234492]

I've heard the second derivative measures concavity, but how exactly is it quantified ?

[Anonymous No.9234503]

>>9233533
Calculus stands for infinitesimal calculus which is an umbrella term for differential calculus and integral calculus. so calculus is just a branch of analysis which studies the theory of differentation and integration (for example you can have calculus on manifolds or on infinite-dimensional vector spaces). analysis is a larger field which includes measure theory, functional analysis and other things. this is how we understand things in europe, HOWEVER in america they have those "calc I-III" courses where they only learn formulas and then the feared "real analysis" where they first learn about the actual definition of a limit. and so I got the feeling that they think of it as calculus = computations, analysis = theory.

[Anonymous No.9234592]

>>9234492
>0 is convex and <0 is concave, or the other way around

[Anonymous No.9234603]

>>9234592
>>9234592
How about, say, 1/2 compared to 1

[Anonymous No.9234613]

>>9234603
what don't you draw a few quadratic functions and see for yourself

[Anonymous No.9234670]

>>9234603
Around a you have that [math] f(x) \approx f(a) + f'(a) (x-a) + \frac{f''(a)}{2} (x-a)^2 [/math] .

The only term that gives "curvature" is the last one and it represents a parabola. If the coefficient is possitive then you have the usual parabola and if negative you have a flipped parabola.

[Anonymous No.9234673]

>>9234603
>>9234670
and the smaller the derivative, the wider the parabola.

[Anonymous No.9234747]

>>9223313
Laugh at me as you will, where does the 12/13 come from? I tried inputting tan^-1(5/12) and that doesn't get the result.

[Anonymous No.9234750]

>>9234747
[math]13^2 = 5^2 + 12^2[/math]

[Anonymous No.9234759]

>>9234750
Huh? Why are we allowed to do that then, I mean surely the entire point of tan^-1(5/12) is that you tack it onto u for whatever the initial speed is, you can't just square both things, I mean is there a proof or something? That just sounds completely out of nowhere.

[Anonymous No.9234770]

>>9234759
[math]\tan \theta = \frac{5}{12} \iff \cos \theta =
\frac{12}{\sqrt{5^2+12^2}}[/math]

[Anonymous No.9234774]

>>9223313
Mathematical morphology....

[Anonymous No.9234783]

>>9234770
Right, I'm just trying to rationalize this here;
>We cannot use tan properly given that the initial speed is simultaneously the hypotenuse whereas tan measures opp/adj. Thus we have to convert it to cos, this being done by taking opp/hyp.
>opp = 12 so we just need hyp
>use Pythagoras theorem for hyp thus becoming stuff
Is that it? Because that sounds easier than it should be when one thinks it through, think I might just greentext through stuff when I'm in doubt now given how much easier it is to think things out. Sorry for coming off as a retard.

[Anonymous No.9234801]

>>9233639
Where can I learn all of these terms and how to apply them real quick, they sound awesome. I wouldn't mind a ordering a Hodge dual for breakfast.

[Anonymous No.9234840]

>>9234801
Quantum field theory and topology by Schwarz.

[Anonymous No.9235037]

I have rather general question.

What are some things that set theory cannot express that can be expressed by other theory?

Im not interested in things set theory could express unfeasibly.

[Anonymous No.9235087]

is logic a meme?

[Anonymous No.9235110]

>>9235087

No, logic is very important.

[Anonymous No.9235111]

>>9235110
how so?

[Anonymous No.9235263]

>>9235111
so you don't go batshit if you can't prove a hypothesis like cantor did

[Anonymous No.9235279]

>>9234840
Thank-you very much anon. How would you recommend learning the material presented in this book? Would it be advisable to memorize every formula? Also concerning methodology is there any way I can practice using the material presented to further understand it for further study. Problem I've had with mathematics is aside from textbook material I've had no understanding of where to really start or how to "read" mathematical literature in terms of pacing and revisiting passages. I'll make sure to read this starting tomorrow (as I am currently reading though Heraclitus' Fragments). Being rather elated and forgive me for this ridiculous degree of pettiness but here's a hug *hug*.

[Anonymous No.9235282]

>>9235279
>Thank-you very much anon. How would you recommend learning the material presented in this book? Would it be advisable to memorize every formula? Also concerning methodology is there any way I can practice using the material presented to further understand it for further study. Problem I've had with mathematics is aside from textbook material I've had no understanding of where to really start or how to "read" mathematical literature in terms of pacing and revisiting passages. I'll make sure to read this starting tomorrow (as I am currently reading though Heraclitus' Fragments). Being rather elated and forgive me for this ridiculous degree of pettiness but here's a hug *hug*.
cringe

[Anonymous No.9235297]

can someone help me with regular expressions? I'm not-understanding how to make one which will detect if a string has an even number of a's and an even number of b's. (which the language being just {a, b} )

I can get how to make a regular expression for an even number of a's, it could be like this:
( b* a b* a b* )* + b*
or even
(((aa)*b*)+(ab*a))*

but every try at making one for both even num of a's and b's doesn't balance the two, I cant really combine either individual regex since they both count on the other char.

[Anonymous No.9235320]

>>9235279
In order to appreciate some of the results of that book you need some physics background. If you don't have that then you need to start from the ground up with Hatcher or Lee or something.

[Anonymous No.9235321]

>>9235297
I don't think that's possible. Remember how limited regular expressions are; there's no mechanism for keeping a 'count'.

[Anonymous No.9235325]

>>9235320
How much would you say? I mean I took an A-level in physics though I wasn't particularly good at it (flunked the subject due in large part to spreading myself way to thin). What level of physics are we talking about here and again would I need to do questions to really understand it or just read through textbooks and get a plain understanding of it?

[Anonymous No.9235331]

>>9235325
I'd say at least Landau-Lifshitz level CM, CFT and QM.
Yes you would need to do some exercise problems. Usually if I could immediately come up with a proof sketch for an exercise I skip the question but that's just how I work.

[Anonymous No.9235337]

>>9235331
Right. I'll read through these books. How long would you say it would take to gain at least a half-decent understanding of Field Theory for someone who has very little knowledge on the subject and what tips can you give? I'll read 10 pages per hour and do what I can to best memorize the formulas as quickly as possible.

[Anonymous No.9235342]

>>9235321
>>9235297
what about

[ (a+b)(aa+bb)*(a+b) ]*

but what about a case where it starts with an a and ends with a b which throws it off? can we do some NFA nondeterminism and assume that wont happen

[Anonymous No.9235384]

>>9235321
Think of automata, you can keep any *finite* amount of memory, just nothing infinite. He just wants to remember parity, that's 2 bits of information. So yes, it's possible. Also it's closed under intersection so if you can do it for a and for b separately, you can do it for both.

>>9235297
Writing the obvious automaton and converting it to a regex, I get
b(aa)*b + (a+b(aa)*ab)(bb+ba(aa)*ab)*(a+ba(aa)*b)
I don't think you can simplify it much but I didn't think about it a lot, maybe i'm wrong.

[Anonymous No.9235390]

>>9235342
ab is in that language. Or aaab, or abbb. You can't make sure the (a+b) is gonna be the same at the beginning and at the end.

[Anonymous No.9235393]

>>9235384
big star missing in that expression, it should be
[ b(aa)*b + (a+b(aa)*ab)(bb+ba(aa)*ab)*(a+ba(aa)*b) ]*

[Anonymous No.9235397]

>>9235337
>How long would you say it would take to gain at least a half-decent understanding
Who knows. Maybe half a year.

[Anonymous No.9235409]

>>9235397
Is there a flow-chart for this kinda thing like on /lit/? I'll go as fast as I can to understand this and obtain some flimsy degree of self-worth though it will probably take me way longer than needed to properly understand things. We'll see what happens. I'm rather enjoying these "test (no.)" images by the way, they seem so warm and comfy.

[Anonymous No.9235418]

>>9235409
Don't think so. You coud search on the internet for a reading list but that depends on what you want to study.

[Anonymous No.9235484]

[Anonymous No.9235533]

Is there any notable difference in content covered by Spivak's Calculus and Tao's Analysis I?

[Anonymous No.9235536]

>>9235533
>Is there any notable difference in content covered by Spivak's Calculus and Tao's Analysis I?
try looking at their table of contents

[Anonymous No.9235650]

>>9235393
I don't think this works for a string like ababab

[ b(aa)*b + (a+b(aa)*ab)(bb+ba(aa)*ab)*(a+ba(aa)*b) ]

- going for right side
- first concatenation: (a+b(aa)*ab) left side: a
- second concatenation: (bb+ba(aa)*ab)* : do zero times
- third concatenation: (a+ba(aa)*b): right side: bab
currently have computed : abab out of original string ababab, still need to compute ab

~~ second loop of entire regex ~~
- computer right side, which is ; (a+b(aa)*ab)(bb+ba(aa)*ab)*(a+ba(aa)*b)

- first concatenation: (a+b(aa)*ab) left side; a
- second concatenation: (bb+ba(aa)*ab)* : do zero times

( have computed so far: ababa, original string: ababab, need one more b)

- third concatenation: (a+ba(aa)*b) left doesnt work, and right doesnt either,

[Anonymous No.9235669]

>>9235650
wait im a dumb fuck the point of the regex is that it only accepts strings that have an even number of a's and an even number of b's

lets say were trying it with the string abababab, an even number of both, should be accepted


[ b(aa)*b + (a+b(aa)*ab)(bb+ba(aa)*ab)*(a+ba(aa)*b) ]

- going for right side
- first concatenation: (a+b(aa)*ab) left side: a
- second concatenation: (bb+ba(aa)*ab)* : do zero times
- third concatenation: (a+ba(aa)*b): right side: bab
currently have computed : abab out of original string ababab, still need to compute abab

and u can just repeat it so it works for that string

[Anonymous No.9235679]

>>9235409
You're not only gonna fail anon, you're gonna crash and burn.

You're eager, that's good, but don't let that take away from the actual difficulty in those subjects, and know that a reading in the way you're thinking of doing is going to give you only a cursory understanding of the material, which in turn will make you unable to understand the material less than 20-30 pages later in any book. This will make you lose all progress and hope, and will make you, as I said, crash and burn.

For that very reason, you're going to need handholding to the point where you can make more than just baby steps and baby decisions on what you want to study. This process is called the acquisition of mathematical maturity, and it is something that takes years of honing to fully benefit from it.

For that reason, the very first thing you need to learn is logic and proofs. However, many students feel unmotivated to study these without any math background, which is why usually "easy" and applicable subjects, which are computationally heavy, are studied at the start of one's degree in math, namely calculus and linear algebra. Computation is not an integral part of mathematics, but it does help to acquire some maturity.

On that note, your best chance is to attempt some of the meme lists that get passed around in /sci/. You should attempt something like Stewart Calculus -> How to Prove it -> Axler Linear algebra ->Tao Analysis to start.

On the physics side, something like University Physics Young Freeman ->Taylor Classical Mechanics -> Quantum mechanics Griffiths -> LL CM

Just acquiring an actual basis to start exploring deeper stuff by doing all these books should take you >1 year

Good luck

[Anonymous No.9236187]

>>9233387
this

[Anonymous No.9236241]

Given:

f '(x1) ≡ limit Δx->0 [ (f(x1+Δx) - f(x1))/Δx ]

Prove:

f '(x^-n) = -nx^n-1

[Anonymous No.9236363]

>>9233645
If you're thinking about the dude from Cabela's, yes I did.

[Anonymous No.9236376]

>>9230011
>https://arxiv.org/pdf/1710.04503.pdf
Found it


" We proceed the [math]3x+ 1[/math]-procedure on [math]x[/math].If [math]x[/math] is even, then [math] x_1 = \frac{1}{2} x [/math] and [math]x_1< x[/math]. Therefore, by the induction hypothesis, the [math]3x+ 1[/math]-procedure on [math]x[/math] terminates on [math]1[/math]. "

Pretty fucking big assumption that does not work for [math]3n - 1[/math]

[Anonymous No.9236438]

>>9235397
Oh you're back, how's the research going?

[Anonymous No.9236441]

>>9236438
I've been researching the best ways to cook up homeless dogs and it has been going pretty well.

[Anonymous No.9236471]

>>9235679
Thank you for the book recommendations. I will look into them; started that Landau-Lifshitz book and the application of second order differentiation appears to make a greater degree of sense although I'm rather confused as to what these "Langrangians" are, tried searching them and they just appear to be arbitrary constants, in which case using "x" in place seems better to me, though I'm sure I'm missing some of the context.

Looked into limits and they do not seem bad at all, just whatever y-coordinate that can be reached the closer you get to a breakage in a line, or something to that affinity right? I'm going to go through the tutorials innumerable times. I'll read through the first volume in the series today just to get a very basic idea of what concepts are available then go through the books you have suggested; using Khan Academy, the material I'm currently studying and an Advanced Physics textbook to supplement reading.

[Anonymous No.9236593]

>>9236471
what exactly is your educational background?

[Anonymous No.9236603]

>>9236593
Retaking A-levels (economics and further maths) externally at the moment, applying for foundation courses in civil and mechanical engineering. Essentially a moron and are self-teaching as educational reform prevents me from retaking maths/ physics courses at the same or any other institute having failed maths and physics before (can't retake physics due to the coursework). Needless to say not a great background and one that I'm very embarrassed about.

[Anonymous No.9236608]

>>9236471
So are you just going to ignore my advice?

You clearly are nowhere close to even begin to think you understand what a Lagrangian is, considering you don't even know what a limit is.

You don't know what differentiation is.

Try following the list, and no, don't "supplement" with an advanced physics textbook, because you don't know basic physics

[Anonymous No.9236625]

>>9236603
jesus dude listen to >>9236608 please

[Anonymous No.9236627]

>>9236608
Right, I'll read through the list. And the "advanced" is in reference to the advanced level which I have previously taken and whilst old was nonetheless designed for the specification.

[Anonymous No.9236630]

>>9236603
also which a levels did you pass in?

[Anonymous No.9236634]

>>9236438

[Anonymous No.9236881]

would this be a valid proof for the chain rule assuming I proved existence of the taylor polynomial (although i'm pretty sure most analysis classes would proof chain rule before taylor)?
[eqn]
\frac{f[(g(x_0+h)]-f[g(x_0)]}{h} = \frac{f[g(x_0)+hg'(x_0)+\mathcal{O}(h^2)]-f[g(x_0)]}{h}=
\\
\frac{f[g(x_0)]+(hg'(x_0)+\mathcal{O}(h^2))f'(g(x_0))+\mathcal{O}((hg'(x_0)+\mathcal{O}(h^2))^2)]-f[g(x_0)]}{h} =
\\
g'(x0)f'(g(x_0))+f'(g(x_0))\mathcal{O}(h)+\mathcal{O}(h)
[/eqn]
thus
[eqn]
\lim_{h\to 0} \frac{f[(g(x_0+h)]-f[g(x_0)]}{h} = g'(x0)f'(g(x_0))
[/eqn]

[Anonymous No.9236908]

>>9236608
>So are you just going to ignore my advice?
>You clearly are nowhere close to even begin to think you understand what a Lagrangian is, considering you don't even know what a limit is.
>You don't know what differentiation is.
>Try following the list, and no, don't "supplement" with an advanced physics textbook, because you don't know basic physics
Your way of learning isn't the only way.

[Anonymous No.9236915]

Solving equations and inequalities with Absolute Values, I'm a freshman at a hood rat high school were they were too fucking stupid to me in geometry so I'm taking Honor's Algebra, a class I took my 7th and 8th grade year.

[Anonymous No.9236926]

>>9236908
yes but going over fucking landau CM when you dont have a fucking clue what a limit is, or newtonian mechanics for that matter, is actually fucking retarded

[Anonymous No.9237636]

>>9236441
Ah, so you're Korean
>>9236634
Makes sense, last time you were here I remember you saying you were moving, or maybe that was another guy, who knows

[Anonymous No.9237645]

>>9237636
Nah, I'm Taiwanese.
>or maybe that was another guy
I'm the guy who shits up these threads with avatarposting.
You can find examples of my posts here:
>>9233639
>>9234840
>>9235397
>>9236634
I've been banned on multiple occasions but i don't care lmao

[Anonymous No.9237657]

>>9237645
You forgot your avatar.

[Anonymous No.9237969]

>>9237657
I used string theory (which is superior to TQFT) to teleport it through a wormhole lawl!

[Anonymous No.9238031]

>>9236363
>>9233662

You are not the guy who was making a really shit program to test collatz conjecture or that was in another imageboard? Because if it was, it was a big fucking coincidence.

[Anonymous No.9238033]

I'm trying to wrap my head around this real analysis proof about exterior measures. Essentially every finite set is lebesgue measurable and has measure 0.

[Anonymous No.9238037]

>>9236471
Is this a troll?

[Anonymous No.9238049]

>>9238037
I think it's just an overeager 18 year old who was "smart but le lazy" in high school who somewhat came to his senses after failing a couple a-levels.

source: used to be him

[Anonymous No.9238103]

If I have a number of items, and a couple criteria to rank them by, what's a better method of getting the overall "best" one than simply sorting them for each criterion, then summing up the results for each item and sorting the sums?

[Anonymous No.9238152]

>>9238031
>You are not the guy who was making a really shit program to test collatz conjecture or that was in another imageboard?
No.

[Anonymous No.9238174]

>>9238031
>You are not the guy who was making a really shit program to test collatz conjecture or that was in another imageboard? Because if it was, it was a big fucking coincidence.
I'm not a "guy".

[Anonymous No.9238205]

>>9238174
Then fuck off to your Taiwanese subreddits.

[Anonymous No.9238213]

>>9238205
>Then fuck off to your Taiwanese subreddits.
huh?

[Anonymous No.9238307]

>>9223313
the collatz conjecture is fucked
some things man was not meant to know

[Anonymous No.9238313]

Is Khanacademy a good place to learn math?

[Anonymous No.9238315]

>>9238313
>Is Khanacademy a good place to learn math?
No.

[Anonymous No.9238324]

explain this shit to me /mg/

[Anonymous No.9238329]

>>9238324
https://en.wikipedia.org/wiki/Difference_of_two_squares

[Anonymous No.9238345]

>>9238315
Got a suggestion other than college?

[Anonymous No.9238366]

>>9229990
>being this autistic

[Anonymous No.9238638]

>>9238313
no

>>9238345
textbooks
pirate them

[Anonymous No.9238796]

>>9238366
>>being this autistic
What's autistic about asking what Taiwan has to do with my post?

[Anonymous No.9238812]

>>9223313
Is there another thread like this but for non-subhumans?

[Anonymous No.9238817]

>>9238049
if you read her post you'd know she hasn't come to her senses yet

[Anonymous No.9239002]

Reminder to study category theory and study it well if you want your work to be relevant.

[Anonymous No.9239059]

>>9239002
Ok, I just dropped category theory from my list of stuff to study.

[Anonymous No.9239061]

>>9239002
But category theory is irrelevant to most of mathematics.

[Anonymous No.9239069]

>>9239061
What makes you think "most of mathematics" is actually mathematics? Most of the garbage studied by people can't really be called that.

[Anonymous No.9239071]

>>9239069
>What makes you think "most of mathematics" is actually mathematics?
If most of mathematics wasn't mathematics then it wouldn't be most of mathematics.

[Anonymous No.9239077]

>>9239061
I challenge you to name a singe field of _mathematics_ (it's important to note that I am talking solely about mathematics) in which category theory is irrelevant.
>>9239071
Indeed, so your post is actually wrong.

[Anonymous No.9239078]

>>9239061
I sort of understand what you are saying but also...
name a major branch of math that doesn't overlap with category theory

[Anonymous No.9239079]

>>9239077
>Indeed, so your post is actually wrong.
What's wrong about it?

[Anonymous No.9239084]

>>9224942
??? and what are the morphisms?

[Anonymous No.9239087]

>>9239078
>name a major branch of math that doesn't overlap with category theory
Analytic number theory

[Anonymous No.9239088]

>>9239084
>??? and what are the morphisms?
Take a guess.

[Anonymous No.9239096]

Discrete mathematics for my CS degree, also how would you prove the exercise 58? I understand it but dont know how to phrase it nor how to prove it using all the information

[Anonymous No.9239097]

>>9239096
show that n^2 fits the given definition of an even number

[Anonymous No.9239098]

>>9239087
So the "sort of understand" was me thinking pretty much of number theory qua number theory (specific results about specific with specific sets of numbers etc.). I think it might be an isolated case.

But to say its totally disconnected is still sort of extreme. The mathematical structures used to analyze these number theory problems are surely categorifiable, e.g. can study things from the point of view of meromorphic functions, arithmetic geometry, etc.

[Anonymous No.9239099]

>>9239096
Really now?
n=2k ==> n^2=2(2k^2)

[Anonymous No.9239100]

>>9239088
deductions?

[Anonymous No.9239105]

>>9239099
that actually makes sense but shouldnt it be just (2k)^2 instead of 2(2k^2) if not why?

[Anonymous No.9239106]

>>9239079
It claims there are fields of mathematics where category theory is "irrelevant".

[Anonymous No.9239108]

>>9239105
...

[Anonymous No.9239109]

>>9239106
>It claims there are fields of mathematics where category theory is "irrelevant".
Which is true, so what was wrong about my post?

[Anonymous No.9239110]

>>9239087
>Analytic
Instant trash.

[Anonymous No.9239111]

>>9239109
Are you implying it is both true and false? Sure, in that case it's true.

[Anonymous No.9239114]

https://mathoverflow.net/questions/165405/category-theory-free-areas-of-pure-math-category-theory-loaded-areas-of-app
>Most areas of dynamical systems, Ergodic theory, spectral theory, nonlinear PDEs, and probability
> Low dimensional topology/geometry too
>geometric PDE's

[Anonymous No.9239118]

>>9239111
>Are you implying it is both true and false?
Can you point out where I implied it was false?

[Anonymous No.9239119]

>>9239114
>"pure math"
Stopped reading right there. It's pop-sci garbage. There is no other kind of math.

[Anonymous No.9239121]

>>9239119
>There is no other kind of math.
There's also applied math.

[Anonymous No.9239122]

>>9239121
I'm pretty sure you can't say "there is" if it can't be shown to exist.

[Anonymous No.9239124]

>>9239122
>I'm pretty sure you can't say "there is" if it can't be shown to exist.
Irrelevant since it can be shown to exist, see https://en.wikipedia.org/wiki/Applied_mathematics for example.

[Anonymous No.9239126]

>>9239118
see >>9239071

[Anonymous No.9239127]

Reminder not to give attention to the mentally ill shitposter. It's for his own best. t. his therapist

[Anonymous No.9239128]

>>9239124
>wikipedia
Ignored, try better next time.

[Anonymous No.9239129]

>>9239126
Where in that post did I imply it was false?

[Anonymous No.9239131]

>>9239128
>Ignored, try better next time.
https://www.seas.harvard.edu/applied-mathematics

[Anonymous No.9239135]

>>9239002
>people who don't study category theory
Do they still exist? Or aren't they an endangered species?

[Anonymous No.9239136]

>>9239135
>Do they still exist? Or aren't they an endangered species?
Category theory is irrelevant to most of mathematics.

[Anonymous No.9239137]

>>9239131
Ignored, try better next time.

[Anonymous No.9239139]

>>9239136
That is one of the stupidest ideas I have ever heard.

[Anonymous No.9239379]

>>9239135
> people who study it
are even worse
CT is a bunch of definitions, and the natural language / abstraction for known things
abstract nonsense is well known since the age of stone
you don't even need to prove anything, it is either trivial or it just work

[Anonymous No.9239393]

>>9239379
It's a way to quickly get the trivial things out of the way, if you aren't capable of that you're simply retarded and should go study trivial garbage like analysis.

[Anonymous No.9239646]

>>9239379
Is this somehow supposed to be bad?

[Anonymous No.9239945]

>>9238817

>somewhat

at least's he's trying

[Anonymous No.9239964]

>>9223313
>>9223313

Does anyone know where i can find the AoPS Book pdfs without buying em?

[Anonymous No.9240095]

A metal requires a photon of wavelength 250. nm to just eject an electron with no kinetic energy. If a photon of wavelength 200. nm strikes the metal, what will be the velocity of the electron that is ejected?
Question 2 options:

6.6 x 105 m/s

3.2 x 105 m/s

4.7 x 104 m/s

8.2 x 106 m/s

2.1 x 106 m/s

[Anonymous No.9240472]

>>9239964
libgen or piratebay

[Anonymous No.9240483]

>>9239393
you sound like one of those individuals whose analysis background consist at most of 'mit retarded analysis 101'

>>9239646
in my experience it is, people who study(memorize) ct without background don't really understand a thing, are unable to even say a thing without reading it from a book, like that homological algebra teacher who always replied 'i have never thought about it'

[Anonymous No.9240683]

>>9240483
>you sound like one of those individuals whose analysis background consist at most of 'mit retarded analysis 101'
Nope, even that would be above my level. Why would I want cancer from studying even basic analysis?

[Anonymous No.9240688]

>>9240483
>without background
Without what background?
>don't really understand a thing
What does "understanding" constitute? How are you able to detect it?