Infinity = 0.
You can not prove me wrong.
If I ask you to show me 3 you can take out three crayons and line them up to demonstrate.
You can do the same with any other number BUT if I asked you to show me infinity you wouldn't be able to show me by lining up your crayons. The same goes for 0. Therefore they are equal
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Interesting. This actually works rather well in a universe that is cyclic. You go infinitely far then you end up where you started.
This would immediately fix a lot of problems in theoretical physics.
Infinity isn't real
maths can't go on forever, you'll hit a limit, either by running out of matter to calculate/display the number or you'd run out of time saying/reading it
i wonder what the last number possible is though
what would Zeno say?
In higher category theory, this notion isn't so bad. You end up with something like a relation making the initial object the homotopy colimit of certain large diagrams, and end up with approximations to higher abelian categories (exhibitions of stable cohesion).
In some sense, spaces behave this way modulo homotopy. That's why the infinity sphere is contractible.
The formation of stable homotopy categories is one way to formalize the idea. In relation to the function field analogy and the Goodwillie calculus, it's why stabilization unifies the three poles 0,1, and ∞ that show up in dessin d'enfant theory, and you pass from ∞-topoi to stable ∞-topoi. If one is some sort of higher geometry over a field, the stabilization is higher geometry over the field on one element.
I'm writing a paper that looks at some of these ideas right now. Maybe this thread won't turn out to be pure shitposting?
very interesting idea but i am an undergraduate pleb with no good input
>Maybe this thread won't turn out to be pure shitposting?
I was literally shitposting though.
>tfw people don't even recognize your shitposts
I don't know if this is good or bad.
If I have infinitely many crayons, I'd just take infinitely long to line them up. That's not prohibited in your dumb example.
okay maybe you could take an infinte amount of time but if you include ALL NUMBERS(including negative numbers) then infinity is equal to 0.
...
Infinity is the limit of a divergent series, zero is the limit of a convergent series; therefore, the two are not equal. Your example is false equivalence.
Go back to school.
Continuing because I can't believe how retarded you are Because then you would be saying that the series
[math] \sum_{i = 1}^{\infty]n = \sum{i = 1]^{\infty]0 [\math]
Which clearly isn't true because none of the partial sums are equal, and since the first sums to tends towards infinity and the second tends towards zero, zero and infinity cannot be equal.
Whoops!
[math] \sum_{i = 1}^{\infty]n = \sum{i = 1]^{\infty]0 [/math]
>zero is the limit of a convergent series
then 0 = 1 since the geometric series converges to 1
[math] \sum_{i = 1}^{\infty]n = \sum{i = 1}^{\infty}0 [/math]
Point is, you're retarded, but one last try for the gold.
where do I sub in my crayons into the equation?
There are multiple geometric series, not all of which converge to one. I should have said, "zero is the limit of A CERTAIN convergent series", like I posted later.
If you would like yet another example of why you're wrong, consider the following:
An infinite number of crayons can be put into a bijective correspondence with the natural numbers. Zero crayons, or rather an empty set, does not have a bijective correspondence to the empty set. And since the two sets have notably different cardinalities, zero =/= infinity.
>There are multiple geometric series
no there's not
Yes, there are. A geometric series is a series with a constant multiplicative ratio. You can begin or end the series anywhere you'd like, and they don't all converge. In fact, there are infinitely many more divergent series than convergent ones, which I can also prove to you since you clearly have no understanding of higher math.
What grade are you in?
actually -1/12
Stop with your meme maths
Also not true. All you've proven is that a sum equals zero, which says nothing about the number of terms in the sum. Consider the partial sum -1 + 1 -2 + 2 - 3 + 3 = 0, but, according to your logic, this means that 6 = 0, which it categorically doesn't. You can prove 6=/=0 a number of ways, including the algebraic identity definition. Choose one, and I'll do it for you.
geometric series is 1/2 + 1/4 + ...
I always thought infinite was a relative term.Like I would say that the earth's circumference is infinitely big for a bacteria.
>spot the engineer
π = 0
You can not prove me wrong.
If I ask you to show me 3 you can take out three crayons and line them up to demonstrate.
You can do the same with any other number BUT if I asked you to show me π you wouldn't be able to show me by lining up your crayons. The same goes for 0. Therefore they are equal
You have conclusively shown that 0 and infinity share a characteristic: hard to express by lining up crayons
infinity is not a number, get over it. It's like asking how does a derivative smell like.
[math]S = \cdots + x^{-2}+x^{-1}+x^{0}+x^1+x^2 +\cdots[/math]
[math]xS = \cdots + x^{-2}+x^{-1}+x^{0}+x^1+x^2 +\cdots[/math]
[math]S=xS[/math]
since x is arbitrary, [math]S=0=\infty[/math]
No, that's *a* geometric series.
en.m.wikipedia.org
b8/10, you reeled me in.
>what are hyperreal numbers
Obviously you have to take potential in hand, infinity is an absolute; limited to the label and definition.
humans categorize logics and define true phenomenon with logic limited to literature.
infinity describes endless information with no meaning only the whole to show for.
these human concepts are limited to the perception inbedded into our intelligence, potential is the most accurate way of describing phenomenon not limited to the characteristics we label them with.
If quarks can have flavour why can't derivatives have odor?
>You can do the same with any other number
Not if it's greater than 10^200
By definition, adding infinity to a number equals that number. If you add infinity to a number, it doesn't equal that number. Therfore, infinity does not equal 0.
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>two things have a property that is the same
>therefore, those two things must be equal
infinity is not a number
Does this relate in any way to norms? Because the "sphere" in the ∞(=2^∞)-norm is the dual of (and in 2D is actually isometric to) the sphere in the 1(=2^0)-norm. And in the "middle" you have the 2(=2^1)-norm which gives the standard sphere. I have been wondering if there is a way to explain this duality, and why those three norms are so special.
That's not immediately related to what I was talking about (since I am merely describing homotopy types as spaces), but the duality you describe I think is related to Poincaré duality in some way. I would supply you with links, but maybe check out the nLab page on norms. It's an interesting topic!