/sci/ - Science & Math

>>12088145
depends on how you get infinitely many of them

>>12088145
no

>>12088145
20*inf=inf

>>12088150
prove it

>>12088145
Urogynecologist speaking, possibly.

>>12088155
https://en.wikipedia.org/wiki/Georg_Cantor

>>12088145
u havent realized by now that math is just logical rules invented by humans? anything can be equal to anything if you say so

>>12088193

>>12088193
the smoothest brain

>>12088193
Dae 2 + 2 = 5???

>>12088145
both are infinities

You have to use the limit of infinities to understand this question. If you do not understand limits then gladly ask away.

the limit of 1/∞ = 0
the limit of ∞/1 = ∞
the limit of 3∞ = ∞
the limit of -5∞ = ∞

the limit of both 1∞ and 20∞ are the same, but!

lemme give you this example (image)
y = (x3-1)/(x-1)

if you look for the value of y if x is 1, is undefined because the value is 0/0

but if you take the limit of y as x approaches 1, the value is 3

meaning the limit of 1∞ is equal to the limit of 20∞, but 1∞ may or may not be the same as 20∞

I hope this answers your question anon, you can't simply multiply and compare infinities to each other without special functions. Unfortunately for this one the answer is syntax error.

>>12088145
lim(x->inf) (20x)/x = 20

>>12088145
1 + 1 + 1 + 1 + ... = (1 + 1 + ... + 1) + (1 + 1 + ... + 1) + (1 + 1 + ... + 1) + ... = 20 + 20 + 20 + ... = -1/12 = i/sqrt(6) = infinity

>>12088247
>limit of -5∞ = ∞
this is a mistake sorry, it should be -∞

>>12088145
Personally I would pay more money to have infinite $20 bills than infinite $1 bills.

>>12088145
Yes, they would both be worthless

>>12088145
False. The infinite number of $20 bills would be worth more. Because our earth is finite, we can only fit a finite number of bills on our planet. $20 and $1 bills are the same size, so filling the earth with $20 bills would result in greater value.

>>12088303
>imagine infinity
>NOOOOOOOOOOOO INFINITY CAN'T EXIST NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

>>12088145
Yes, and both would be cheaper than toilet paper and it will mean for US dollar to have no value beyond toilet paper.

>>12088315
Ah yes, the brainlet replies with a frog image, like clockwork. The point is not that infinity can't exist, it's that they wouldn't be worth the same because "value" is determined by us humans.

>>12088291
>pay money
>to have infinite bills

>>12088320
Literally not what he said though, all he talks about is how the earth is finite, not that value is determined by humans.

And I will have you know that I will frogpost whenever I want to faggot.

>nobody itt referencing zeta function. y

>>12088323
infinite bills, not infinite storage

>>12088335
>Literally not what he said though, all he talks about is how the earth is finite, not that value is determined by humans.
Impressive, so you did read my post! Unfortunately, you forgot to actually think about it.
What is an infinite stack of bills worth to us humans? Only as much as we can even fit on our planet right now, right? There's no point in us determining the value of dollar bills that are floating in space light years away from us. So it only makes sense to think about dollar bills on earth, and in this case picking the $20 bills is obviously the choice that is 20x better.

>>12088145
yeah, because they're only worth toilet paper at that point.

>>12088351
Based economics Chad

>>12088351
so more than gold?

>>12088348
You're not making a deep point. This whole thread is retarded, as per usual on /sci/.

Here I can say something retarded too:

>If you had so many dollar bills that they would litterally be lying everywhere on the earth, they would both be equally worthless pieces of paper. We'd probably use them as a fuel source! Isn't that deep?! Think about it!

>>12088303
>problem involves hypothetical scenario
>"lemme tell you why that couldn't actually happen"

Do you want to tell everyone that the Planck length disproves the existence of the real numbers next?

>>12088303
>we can only fit a finite number of bills on our planet.
who said anything about having to store the bills on earth?

>>12088145
Yes. You can group the $1 bills into piles of 20 and there would be exactly as many* piles of $1 bills as individual $20 bills. This quantity is denoted [math]\aleph _0[/math]

*formally, this means you can create a bijection between them https://en.wikipedia.org/wiki/Bijection

>>12088247
Not a number, and not a limit.

>>12088145
Infinity isnt a number

>>12088154
No. you are basically what is 20 times larger than infinity which is undefined

>>12088145
>is this mathematically true?

no, it is not.

>>12088155
>prove it

1 * infinity = infinity
20 * infinity = infinity

therefore 1 = 20, which is wrong.

>>12088669
>Infinity isnt a number

correct, infinity is a concept, not a number.

>>12088767
[math]\frac{\infty}{\infty}\neq 1[/math]

>>12088767
continued....

forgot the second half of the proof.

> 1 * infinity = infinity
> 20 * infinity = infinity

Therefore:

infinity / infinity = 1

or

infinity / infinity = 20

which is it?

>>12088145
Yes because for any [math]n\in\mathbb{N}[/math] the series [math]\sum_{i=1}^{\infty}n[/math] diverges

>>12088799
2 diverging series does nor equate to being the same or equal

>>12088810
Yes but the question was about the total value. You can say for both cases it is undefined or both ar infinite, the value is "the same":

>>12088791
You are such a retard.
[math]\frac{\infinity}{\infinity}=\mathrm{undefined}[/math]

>>12088850
no shit it's undefined, that was my whole point.

the multiplication operation isn't reversible with division to arrive at the original number.

>>12088850
>>12088855
actually, now that I think about it...

infinity / infinity = 1

because infinity can fit within infinity precisely once.

however, as a sort of abstract concept, using infinity in mathematical operations is a bit foolish.

>>12088850
\infty you phoneposting faggot

A bag with a infinite number of 20s in it would be worth more than a similar bag of 1s because you could pull money out of it faster. They would have the same amounts of money, but they would not be worth the same.

>>12088145
The infinite 20 dollar bills would have the extra worth of not having to handle so many one dollar bills.

>>12089282
that's not actual worth

>>12088145
That's like saying both of the same times zero would equal the same amount.

>>12088145

Its true. They are both worth nothing.

>>12088791
1*0 = 0
20*0 = 0

therefore 0/0 = 1 = 20
HUUUURRR HUUUUUUUURRRR DUUUHHHH

fucking faggot

>>12088145
Yes, they would be equally worthless. Fuck fiat currency.

>>12089288
How is it not?

>>12088690
you are basically retarded

https://youtu.be/i7c2qz7sO0I?t=1m15s

>>12088862
1/inf = 0
1 + inf = inf
1- inf = -inf
inf + inf = inf
inf/inf undefined
inf-inf undefined
1^inf undefined

you can't do everything with inf as with a number, doesn't mean you can do nothing tho

>>12088886
>faster
>numbers have clocks on them
hurr durr

>>12090468
>1 + inf = inf

When will people learn that subsets of infinity exist?
2 * infinity is greater than infinity, even though both have no limits.

>>12090482
[math] \displaystyle
\lim_{x \to \infty} \dfrac{x+1}{x} =
\lim_{x \to \infty} 1+ 1/x = 1+0 = 1
[/math]

>>12090695
2(1+2+3+...) = 2+4+6+...
only the even numbers is larger than all the numbers?

>>12090757
cute but irrelevant, figure out why

>>12090880
because you are home schooled?

>>12090695
>2 * infinity
So, infinity?

>>12090764
I wonder...
Is 2(1+2+3+...) the same as 1*2+2*2+3*3+... ?

>>12091059
what else?

>>12091068
Well, I mean, in the first case you're multiplying the end result, while in the second case you're multiplying each number while adding them.
Sure the end result might be the "same" because it's infinite and all that, but are both infinities really equal?

>>12091080
>but are both infinities really equal?
yes

>>12088145
If money was infinite it would be worthless, so it's correct. Both are with $0.

>>12090764
1+2+3+... isn't the same as 2+4+6+...
I stated that 2x =\= x, while you're stating that 2x = y

>>12091105
>1+2+3+... isn't the same as 2+4+6+...
wrong, both are inf

>>12091117
They are both infinities, yes, but they're different subsets of infinites and are therefore not equal.

>>12091141
what is "subset of infinity" ?

yeah but using the $20 bills would make you rich faster

>>12090464
>"Math is really into rules"
Fucking women, that's not how you talk about math or any scientific topic.

>>12090468
1^inf is definitely = 1 you idiot

>>12088149
Correct

>>12088145
Not true. Consider that you get a dollar bill every second and a twenty dollar bill also every second. Then after [math] x [/math] seconds you will have [math] x [/math] one dollar bills and also [math] x [/math] twenty dollar bills. The worth of each pile will be [math] 1 × x [/math] for the one dollar bills and [math] 20 × x [/math] for the twentt dollar bills. Now consider the value of their ratio as [math] x \to \infty [/math] it is:
[math] \lim \limits_{ x \to \infty} \frac {20x}{x} = \lim \limits_{ x \to \infty} 0 = 20 [/math]
Therefore the twenty dollar bills worth (as expected) 20 times more than the one dollar bills. You can easily show that if you got a twenty every 20 seconds it would worth the same. It does depend on how you get infinitly many of them.

>>12091158
>limx∞20xx=limx∞0=20limx∞20xx=limx∞0=20
I meant [math] lim \limits_{ x \to \infty} \frac {20x}{x} = \lim \limits_{ x \to \infty} 20 = 20 [/math]

>>12088145
Proof.
Let's asign our 1$ and 20$ bills some serial numbers. Let's start with 1,2,3, ad infinitum...
Now, let's imagine, we're mapping each 20 dollar bill to a heap of twenty 1$ notes. That means, first twenty dollar bills gets mapped to #1 20$, serial numbers 21-40 to #2 20$ etc. We have enough one dollar bills to do so, so there cannot be less money in 1$ bills stack.
The other way it's trivial, there's no less money in 20$ bills than 1$.
This means they're equally infinite.

>>12091162
[math] \lim \limits_{ x \to \infty} \frac {20x}{x} = \lim \limits_{ x \to \infty} 20 = 20 [/math]

>>12091155
it's not you retard. why should it be 1?

>>12091144
An infinity has only one value: infinity.
For example, 1+1+1+... is infinite and 2+2+2+... is also infinite.
But when looking at the make-up of the infinities, we can clearly see that the first infinity contains only 1s, while the second only contains 2s.
That's how you differentiate between subsets of infinities.
The make-up of the first infinity is infinitely smaller than the second infinity, even though they're both infinite.
Does that answer your question?

>>12091155
[math] \displaystyle
\lim_{x \to \infty} 1^x = 1 \\
1^ {\infty} ~~ undefined
[/math]

>>12091183
no. what is "subset of infinity" ?