/sci/ - Science & Math

[Anonymous No.5869946]

Let me start off by saying I swear I'm not trolling. I just had a thought:

Okay, so we all know that when you divide by zero it is impossible. Why? Because any number multiplied by zero yields zero; therefore, it is impossible to discern what (this is concerning 0/0 only, by the way) was originally multiplied by zero. But concerning the fraction 0/0, couldn't there be an answer to that? And wouldn't that answer be a set of ALL numbers (any type: real, complex, etc...in a way it would be the largest infinity)? Am I buttfuck retarded? Is this all an indeterminate form is?

[Anonymous No.5869951]

no

[Anonymous No.5869955]

fuck off imbecile

mathematics a little above that which you have studied has dealt with all the issues you raise.

a) division by zero is "possible" (that is well defined) in many mathematical structures, for example the riemann sphere http://en.wikipedia.org/wiki/Riemann_sphere..

b) 0/0 is easily managed using limits.

stop accepting statements such as "division by zero is impossible" from non-specialists.

[Anonymous No.5869971]

>>5869955
He asked for 0/0, not the limit of it

[Anonymous No.5869978]

>>5869971
Then define it as its limit, or if you have a problem with that, use some non-standard analysis to define it.

[Anonymous No.5869998]

>>5869971
Good point. He just extended the division function as continuous at 0, which isn´t needed, really. One could take the approach to get the division function non-continous

On the other hand, that procedure has been done many times in the past, for example, for irrational exponents. We all know the algorithms to get integer powers (multiply some number by itself n times) and roots (guessing the reverse of that), but we don´t know any way to get, for example, e^e . Because such result was unknown (there would be no way to calculate more than e^(M/N) with M and N integers) and it seemed proper for some people to have a result of irrational powers... it has been DEFINED as a continuous function, so e^e = lim ( x->e, x a rational number) e^x

On the other other hand, I'd rather like e^x = 0 for any irrational x. It would make it impossible to differentiate and so. Much more fun.

[Anonymous No.5870680]

>>5869998
Your picture is tautological.

[Anonymous No.5870695]

>>5870680
one usually proves that e^x is equivalent to exp(x), the latter being defined in various ways that don't call for irrational exponents

[Anonymous No.5870738]

>>5870695
what? "e" and "exp" are exactly the same thing. interchangeable. Some people just use exp to avoid confusion of another random variable "e"

[Anonymous No.5870745]

>>5870738
>naivety
They are, but they need to be proven so.

[Anonymous No.5870746]

>>5870738
Not him, but I think e is defined as a number and exp as a function

[Anonymous No.5870747]

>>5870738
Non math major detected.

[Anonymous No.5870761]

>>5870746
Yeah, I assume he meant e^x being the same function as exp(x).

Exp(x) is usually defined as a series or limit. But e^x is a power of the number e.

Everyone but a math fag will accept they are equal, a math fag will prove they are equal.

[Anonymous No.5870774]

>>5870695
For example you can define natural number exponents recursively:
<div class="math">x^0 = 1</div><div class="math">x^{y+1} = x x^y</div>Then define <span class="math">\exp[/spoiler] as a power series:
<div class="math">\exp(x) = \sum_{n=0}^\infty \frac{x^n}{n!}</div>Then prove the existence of its inverse function <span class="math">\ln[/spoiler] (only defined for positive numbers).
Then you can extend the definition of exponentiation to real exponents (with some cases left undefined):
<span class="math">x^y = \exp(y \ln(x))[/spoiler] for positive x
<span class="math">0^y = y[/spoiler] for positive y
<span class="math">0^0 = 1[/spoiler]
And then you'd want to prove that when you plug a natural number in for y, this is equivalent to natural number exponentiation defined previously.
And you would define <span class="math">e[/spoiler] as <span class="math">\exp(1)[/spoiler].

[Anonymous No.5870778]

>>5870774
On the other hand, this is a completely different approach to the definitions than what >>5869998 is suggesting. If you take that approach you could define <span class="math">\exp[/spoiler] as the power series, or you could just define <span class="math">e[/spoiler] and then define <span class="math">\exp(x) = e^x[/spoiler].

[Anonymous No.5870781]

>>5869946

[Anonymous No.5870806]

Assuming you're talking about division by 0 in a field, syntactically, 'a/b' is equivalent to 'a * b^{-1}' which implies that b has a multiplicative inverse. 0 has no multiplicative inverse so any term 'a/0' is meaningless in this context.

[Anonymous No.5870822]

That wouldn't be consistent with the way division is defined for other numbers. Is 6/2 the singleton set {3} containing one real number, 3? No, it is the real number 3. These are different objects.

[Anonymous No.5870828]

>>5870822
Were you replying to me? (the comment above you) If so, I don't think I understand your objection. Why would what I said imply that 6/2 = {3}?

[Anonymous No.5870829]

>>5870828
Nevermind, you're clearly not.

[Anonymous No.5870830]

>>5870828
No, to the OP, who wants to define 0/0 as <span class="math">\mathbb{R}[/spoiler].

[Anonymous No.5871396]

>>5870738
What exp are you talking about? <span class="math">Diff(\mathbb R)[/spoiler] does not even have an exp.

[Anonymous No.5872657]

>>5871396
>Diff(\mathbb R) does not even have an exp.

Then apparently she's not talking about Diff(R).

[Anonymous No.5872675]

Haven't studied that much mathematics yet, but dividing with zero has at least one problem:

Let's just say we have f(x)= 1/x

if x = 0, what happens?
lim x->0- = -infinity (gets smaller and smaller)
lim x->0+ = infinity (gets bigger and bigger)

Yes, in a way you could say you can divide by zero, but what's the anwser then, if you're not just looking at the one situation (lim x->0- or lim x->0+)? That's why you don't devide by zero, at least in so called "normal" maths.

[Anonymous No.5872770]

>>5872675
That's not a real problem. Not all functions are equal to their limit, only functions that are continuous at that point.

[Anonymous No.5873167]

>>5872770
How is a function continuous at infinity?

[Anonymous No.5873176]

Mathematics is not a physical object.
it is not confined by spacial limits or time.
It is drawn from logical thinking alone. That is how maths is proven, that is how it is made. this is why x/0= infinity, -x/0=-infinity
anyway
0/0 is no value out of no value
so, you have all of your values
but the values are equal to zero.
multiply any number by 0 and you return to 0
so no op, no yield.

[Anonymous No.5873764]

>>5872657
That means her post is unrelated to the thread.

[Anonymous No.5875350]

>>5873176
OP doesn't multiply by zero, he divides by zero.

[Anonymous No.5876167]

>>5873167
It is impossible to know. You can never reach infinity.

[Anonymous No.5877635]

>>5876167
Not even on the Riemann sphere?

[Anonymous No.5878856]

>>5873764
I still don't get what she was talking about.

[Anonymous No.5880019]

>>5869955
>fuck off imbecile
>division by zero is possible

oh the irony

[Anonymous No.5880673]

>>5880019
Why is it ironic?

[Anonymous No.5882087]

>>5880673
Because every kid knows that division by zero is impossible.

[Anonymous No.5882106]

>>5882087
I'm not him, but division by zero is actually possible using limits, and also using Riemann Sphere.

[Anonymous No.5882112]

>Let me start off by saying I swear I'm not trolling.

[Anonymous No.5882138]

>>5882106
>replying to the Titanspammer

[Anonymous No.5882756]

>>5882138
Who is that?

[Anonymous No.5884154]

>>5882106
>is actually possible using limits
The limit is not uniquely defined.

>and also using Riemann Sphere
The Riemann sphere is a topological notion and does not preserve algebraic properties.

[Anonymous No.5884847]

>>5873176
>Mathematics is not a physical object.
Troll harder. Mathematics is a pattern of neural activity that occurs within a human brain. This is a simple application of neuroscience that has nothing to do with magic.

[Anonymous No.5886210]

>>5884847
>Mathematics is a pattern of neural activity that occurs within a human brain.

Yet we can describe this pattern by using mathematics. Science is fucking awesome!

[Anonymous No.5887329]

>>5886210
I know.

[Anonymous No.5888694]

We will never know.

[Anonymous No.5888722]

>>5869946
Doesn't 0/0 equal 1?

[Anonymous No.5889319]

Someone has been keeping at least 35 threads alive
by bumping them twice a day. Compare the post times of
>>5870680 >>5871396 >>5873167 >>5873764 >>5875350 >>5876167
>>5877635 >>5878856 >>5880019 >>5880673 >>5882087 >>5886210
>>5888722
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5885545
Write to [e-mail] if you want it to stop.

[Anonymous No.5889546]

>>5888722
We could define it that way.

[Anonymous No.5889550]

>>5888722
i don't understand why dividing by 0 just doesn't yield 0 tbh

[Anonymous No.5889554]

>>5889550
Why do you think it would?

[Anonymous No.5889569]

>>5889554
because if you have 4 pencils and put them in 0 places to be separate, you have nothing but i guess nothing isn't the definition of zero

[Anonymous No.5890603]

>>5889569
>but i guess nothing isn't the definition of zero

Actually it is. Zero is defined as nothingness.

[Anonymous No.5890620]

>>5890603
in that case why isn't anything divided by 0, 0?

[Anonymous No.5891326]

>>5890620
It would not work.

[Anonymous No.5891335]

>>5891326
[citation needed]

[Anonymous No.5893021]

>>5890620
Because we're talking about division and not multiplication.

[Anonymous No.5893034]

>>5893021
by that logic anything multiplied by 0 should equal nothing, not 0

[Anonymous No.5893043]

>>5869946
Let me explain: When you divide a number by a number very close of zero, like 0.00000000000000000000000000000000000000000000000000000000002, the result get's bigger, so, dividing by zero makes the result being the biggest number ever, which doesn't exist, because the numbers are infinite.

[Anonymous No.5893793]

>>5893043
The largest number is infinity minus one.

[Anonymous No.5894912]

>>5893793
But if you add 1, you'll get a larger number.

[Anonymous No.5895747]

>>5893034
>anything multiplied by 0 should equal nothing, not 0

0 means "nothing". That's how it is defined.

[Anonymous No.5896931]

>>5869955
>b) 0/0 is easily managed using limits.

How so?

[Anonymous No.5897791]

>>5894912
That number does not exist.

[Anonymous No.5899240]

>>5897791
It has to exist, if you believe in the axioms of the natural numbers.

[Anonymous No.5899841]

>>5899240
I cannot believe in something that is logically inconsistent.

[Anonymous No.5901069]

>>5899841
Then you cannot believe in logic at all. Gödel proved logic is inconsistent.

[Anonymous No.5901864]

>>5901069
What logic?

[Anonymous No.5903277]

>>5901864
philosophical logic

[Anonymous No.5903295]

>>5889319
Can I just say, I think this is more spam than the post you say are spam. You sage, so you look polite, until one realises that sageing with an image still bumps.

[Anonymous No.5903532]

why hasn't this been deleted?

[Anonymous No.5903536]

>>5903532
Because it is a relevant and very interesting math thread.

[Anonymous No.5903539]

>>5903277
what did godel use to prove his theorems? logic. therefore his theorems are wrong.

[Anonymous No.5903567]

>>5903532
Because there is someone who gets great joy of bumping a few select troll threads once a day to see how long they can last.

[Anonymous No.5903584]

>>5903532
samefags

[Anonymous No.5903747]

>>5869946
>Let me start off by saying I swear I'm not trolling. I just had a thought:
>Okay, so we all know that when you divide by zero
Why did I bother reading this far? 1/10 I guess.

[Anonymous No.5903868]

So, like, man, wtf?
I hope this answers your question.

[Anonymous No.5904032]

>>5903868
It does not help me at all. Could you please elaborate a little further?

[Anonymous No.5905503]

>>5903539
Why did nobody figure this out before? Such an obvious flaw in his proof.

[Anonymous No.5906287]

>>5903539
>logic
I thought he used sophistry.

[Anonymous No.5907947]

>>5906287
What is the difference?

[Anonymous No.5908624]

>>5907947
One of them is more prominent in the physics academia.

[Anonymous No.5910154]

>>5908624
Why is sophistry prominent in the physics academia?

[Anonymous No.5911891]

>>5910154
Because often physicists want to publish their theories even though they don't have evidence.

[Anonymous No.5912854]

>>5911891
Some of them publish theories which are known to contradict the evidence.

[Your Penis No.5913988]

I actually got a good explanation of this once.
My geometry prof broke down what is going on when you do division, the nuts and bolts underneath the quick shortcut we usually use.

What it boils down to is this, division is really multiplication.
Specifically, it's multiplying Thing A by the Inverse of Thing B.
ie: (1/Thing B) <-fraction assuming Thing B is an integer.
If Thing B is already a fraction, then just the inverse.
ThingB=(1/3) then inverse ThingB= (3/1) = 3

Ok, so... what's the inverse of 0? . (1/0)
"I have one nothingth!" doesn't make sense outside of my bank account.
Zero doesn't have an inverse, and that's why you can't divide by it. It's like trying to stir diarrhea with your dog's sense of humor.

Captcha: Strong-beer Societeth

[Anonymous No.5914010]

>>5913988
And what's the inverse of Thing B?

[Anonymous No.5914308]

>>5913988
>doesn't make sense outside of my bank account.

How does it make sense on your bank account?

[Anonymous No.5914912]

>>5869946
Not that hard when using limits. For example,
<span class="math">\lim_{x\to\0}\frac{sin{x}}{x}[/spoiler] yields 0/0, but there are clever tricks to see that the real answer is 1.

[Anonymous No.5914935]

>>5914308
There is 300k deposited a year.

[Anonymous No.5916091]

>>5914935
That's a lot of money.

[Anonymous No.5917502]

>Is this all an indeterminate form is?

Yes, this is what an indeterminate form is.

[Anonymous No.5919125]

>>5914010
ThingB^{-1}

[Anonymous No.5920430]

>>5919125
How do you calculate it? For what values of B does it exist?

[Anonymous No.5921200]

>>5920430
You have to solve for T.

[Anonymous No.5922220]

>>5921200
How do I do this?

[Anonymous No.5923141]

>>5922220
There is some NS-flux, so try to find the Langlands dual group.

[Anonymous No.5924112]

>>5923141
That sounds dangerous. What can we do to reduce the flux?

[Anonymous No.5925461]

>>5924112
Redirect it through a pipe.

[Anonymous No.5926452]

>But concerning the fraction 0/0, couldn't there be an answer to that?

0/0 = 1

[Anonymous No.5927376]

>>5925461
What kind of pipe?

[Anonymous No.5929212]

>>5927376
a bagpipe

[Anonymous No.5930906]

I like the way you think

[Anonymous No.5932188]

>>5929212
That will not help. It is an unstable solution and will decay quickly.

[Anonymous No.5933192]

>>5926452
Or 2.
2*0=0.
0/0=2.

[Anonymous No.5933693]

>>5933192
Does it work with 3 as well? Can we generalize it by induction?

[Anonymous No.5933828]

Fuck you....you broke my brain op...

[Anonymous No.5934767]

>in a way it would be the largest infinity

What if we add +1 to the largest infinity?

[Anonymous No.5935945]

>>5934767
It remains unchanged. That's how large it is.

[Anonymous No.5937462]

You cannot divide by zero.

[Anonymous No.5939307]

>>5937462
Yes, you can. Read the OP. The result is the largest infinity.

[Anonymous No.5940551]

What kind of division?

[Anonymous No.5942464]

>>5940551
Division in the set of all numbers.

[Anonymous No.5942956]

>>5942464
0 is not a number

[Anonymous No.5942971]

>>5937462
Thing is, you can. The answer is undefined. I never understood (simply) why dividing something by one wasn't 1/2, because if you divide something by itself 0 times the answer'd be one. Basic n series. Infinity makes sense, too, just...not as much sense. (imo)

[Anonymous No.5942973]

>>5942971
Sorry, the answer'd be whatever number you divided from.

[Anonymous No.5943113]

>>5942971
>never understood why dividing by 1 wasn't 1/2

[Anonymous No.5943124]

>>5943113
Yeah, because it could be just one slice of any size, meaning it'd be subtracting by fractions. Makes sense verbally, but the deeper you go into it yadda yadda, tired as fuck words jumbled. If you divide something by zero*

[Anonymous No.5943127]

>>5943124
I guess I should've said if you divide something by itself 1 time, a mix match, if you will.

[Anonymous No.5943141]

>>5869955
>b) 0/0 is easily managed using limits.
No it's not.
limit of 1/x as x approaches 0 from the left is negative infinity while the limit of 1/x as x approaches 0 from the right is positive infinity.

[Anonymous No.5943151]

>"Let me start off by saying I swear I'm not trolling. "
Lost my interest with the first sentence so I stopped reading. I only feed trolls. This is National Be Kind To Trolls Month.

[Anonymous No.5943152]

>>5943141
Thats not 0/0 tard, good to see you've watched the khan academy video on limits though

[Anonymous No.5943160]

>>5943152
Well it shows that 0/0 is indeterminate. Unless there's a super seekret way you learn what 0/0 is higher math in which case, enlighten me.

[Anonymous No.5943259]

>>5943160
you are over thinking things.

2n, where n is an integer will always give you a positive number.

2n+1, where n is an integer will always give you an odd number.

from this we can conclude 0 is even.

[Anonymous No.5944417]

>>5943160
>Well it shows that 0/0 is indeterminate.

No, it only shows that 1/0 is indeterminate.

[Anonymous No.5944454]

>>5869946

when any number x 0 yields 0
how can 0 / 0 not yield any number....meaning R ?

C if you are using 0 + 0i
I if you are using 0i

Well I think this deserves a decent treament.
I conjecture one would be working with the mathematics of sets rather than single numbers.

Having a result that is a set breaks the language of simple arithmetic, just as infinity does.

Interesting question.

[Anonymous No.5946593]

>>5944454
If we took the set of largest cardinality and looked at its power set, could it have larger cardinality?

[Anonymous No.5947801]

>>5946593
It can't because it is the largest cardinality.

[Anonymous No.5949203]

>>5947801
We can construct it as the infinite union of repeated power sets.

[Anonymous No.5949292]

>>5949203
fuck off maggot

[Anonymous No.5949299]

you can devide by zero,let me explain so you humans can under s tand

0=0

10= 1+0=10

so 0=9

9/9= 1

those zero devided by zero =1

perfectly logical

[Anonymous No.5949957]

>>5949299
Thank you for the input. Your post is very appreciated.

[Anonymous No.5951208]

>>5949299
Very elegant proof. I tip my fedora to you.

[Anonymous No.5953340]

>>5949299
>those zero devided by zero =1

or -1

[Anonymous No.5954693]

>>5949292
Your post was rude and hurt my feelings. Please be more polite.

[Anonymous No.5956015]

Division by zero can be any number.

[Anonymous No.5956031]

> The function (x,y) -> x/y
good luck extending that to a continuous function.

sauce: http://www.wolframalpha.com/input/?i=x/y

[Anonymous No.5956934]

>>5956031
It is already continuous.

[Anonymous No.5956951]

>>5956934
>>5956934
"on R^2" was implied. Or do you often *extend* functions to a domain on which they are already defined (in this case RxR*)?

[Anonymous No.5956952]

>>5956934
0/10 Not even over the extended reals

[Anonymous No.5956958]

>>5873176
I like this. It's true. Math is like a game were you can make up the rules and test them. If the system breaks down, well, it was your game, and it is neither right nor wrong, it just is. You can say 4 = 5 or there are only bananas and elephants, really theoretical math takes some liberties and foundations tries to distill math to the tiniest of axioms, like the axiom of choice. Imaginary and complex numbers are an example of making rules up and making shit up and having it applicable to the real world. But you can have math that has no application whats so ever, and the super strange thing is that when physics discovers some new property of the universe, the math was done decades ago.

[Anonymous No.5957327]

>>5956952
The extended reals are not the only possible compactification.

[Carbon No.5957344]

>>5869946
moot really needs to purge ALL of the fucking /sci/ janitors because one of them is an extreme faggot and the rest don't do their jobs...

[Anonymous No.5957382]

>>5956958
> physics discovers some new property of the universe, the math was done decades ago
or vice versa

[Anonymous No.5957389]

>>5869946
Dude

0/0 is x/x, so it should equal 1
And yet it's the same as 0*y where y=z/0
So it's 0

There is no answer

[Anonymous No.5957926]

>>5957389
You forgot 0/0 is (42*x)/x so it should equal 42. It is the answer.

[Anonymous No.5957950]

Wheels?

[Anonymous No.5957982]

Can there be a set of only transfinite values?

[Anonymous No.5957988]

It just makes sense. If you have a glass of water regardless of how full it is, how many times can take 0 mL out of it?

[Anonymous No.5958029]

I think there's two ways to define this and the first doesn't really count.

1.) 1/0 could be seen as "1 divided by nothing" if you are dividing one by nothing you are not dividing it at all. Therefore 1/0 is simply 1. This doesn't really count because its just a natural language definition. It's imprecise, informal.

2.) 1/0 is like having "1 part out of nothing" how does one have a piece of nothing?" In a way it doesn't follow the axiom of excluded middle where "something" = all numbers such that the number doesn't equal 0 and "nothing" = all numbers such that the number doesn't equal "something".

[Anonymous No.5959291]

>>5957950
Nobody ever uses wheels, not even in abstract algebra.

[Anonymous No.5959293]

How close can you get to a real number?