Questions tagged [infinity]

Use this tag for questions on the concept of infinity. Don't use this tag merely because $\infty$ appears somewhere in the question.

A lay person might think they know what infinity is, but a mathematician will ask you "what kind of infinity are you talking about, and in what context?"

See the question Is Infinity a number and in particular this answer for a good discussion on a number of things that people sometimes mean when they talk about "infinity" in mathematical terms.

Good questions about infinity will need to be explicit about the context in which the question is being asked; many of the questions already tagged essentially have the answer "The answer is undefined, because infinity isn't an ordinary number" or "Your question can't be answered without giving more information." And there is probably already a different tag covering whatever field of mathematics the question is about.

Please check the questions What is the result of $\infty-1$? and What is the result of infinity minus infinity? before asking questions about doing arithmetic on infinity.

Questions about fallacies involving infinity are on-topic for this tag.

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Counting down by halving to 0

Say that you are counting down from 10. You say how long is left after half the amount of time you said how long was left (Like 10, 5, 2.5, 1.25, 0.125, etc.). Because when you halve repeatedly you can never get down to 0, wouldn't you have to say…
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Infinite hotel +1 guest

Can anyone explain how is it possible to fit another guest in an infinite hotel that is already full? Here's how the explanation (supposedly) goes: A guest arrives at an infinite hotel, where every one of the infinite number of rooms is occupied by…
Ibolit
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Ratio of whole numbers to even numbers

my son came home from school and said that there was a 1:1 correspondence between even numbers and whole numbers. Is that correct? It seems to me that even though they are both infinite, there will have to be twice as many whole numbers as even…
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Is there a way of defining infinity so that it both meets the criterion of being a number as well as being greater than any real number?

This number would not be equivalent to the concept of infinity, but would be a number analogous to that concept. I'd also be interested to how the different ways of doing this (I'm assuming there are many), how they differ, and what their different…
tom894
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$n \rightarrow \infty$ and $x\rightarrow \infty$

If i have $\lim_{n \rightarrow \infty}s_{n}$ for all $n\in \mathbb{N}$ like a sequence and $\lim_{x\rightarrow \infty}f(x)$ for all $x\in \mathbb{R}$, Do $x$ and $n$ tend to the same infinity? i do not know if my question is well asked, i think the…
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Is there a notion of a smallest possible number?

Firstly, yes, you can divide any number and get even smaller one but hear me out. My logic goes as follows: Let there be a number X. This number behaves similiarly to infinity, except it is not infinitely large, it is infinitely small. You could…
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If the law says "Provide a valid solution for 0x = 50, or go to jail", can we avoid being jailed?

Law Stack Exchange has a question about a hypothetical law that everyone is meant to be guilty of breaking. What if a law is literally impossible to follow? While that's an interesting idea, they used an example law which touched on mathematics…
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Devils and Infinity

You are in hell for all eternity and the devil gives you two dollar bills every day with increasing serial numbers. He then takes the dollar bill you have with the smallest serial number. At the end of your infinite stay in hell, do you have…
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Do aleph numbers and infinite ordinals have correspondence?

I mean can we say for example omega squared corresponds to aleph one or something? Are aleph numbers and infinite ordinals completely different? Do cardinals and ordinals become two different sets of numbers when we think about infinity?
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A vertical line in a cartesian coordinate system

Let's say I have points $A(a,a)$ and $B(a,0)$. What is the equation of the line $AB$? If I'm correct the slope is infinite, but it never has a y-intercept. This would give $y=\infty x$, but there are infinitely many lines which should have this…
JohnPhteven
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Proof of $+\infty=-\infty$ (Maybe)

I guess we can agree that $+0 = -0$. Now, after that, I was simply looking at some graphs. The graph of $\tan x$ shows asymptotes at x = $n\pi + \pi/2$. I got to thinking, what if they weren't asymptotes, but actually continuous lines? If I take $0$…
SS_C4
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How to count the number of rebound cycles of a ball in a 1d system after time t, where velocity doubles every rebound

This is something I dreampt up in a physics lab about imagining infinity but I never got round to modeling it. Seems like it could get out of hand pretty quickly! Imagine we have a ball in a 1d system that bounces back and forth between point x1 and…
Nikos
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Ratio when one entity is 0.

What is the ratio between boys and girls in a group with 30 boys and 0 girls? Is it 1:0, 30:0 or something involving infinity and undefined? Can somebody help me out here?
user33984
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Approaching infinities

How big of an infinity can we approach? At first I naively thought about: $$ \lim_{i \to \aleph_0}\aleph_i $$ However, this approaches $\aleph_{\aleph_0}$ which is $\aleph_{\omega}$ Let's define: $$ a_i := \aleph_{\aleph_{..._{\aleph_i}}} $$ Where…
pushkin
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Question about infinity

That might be a silly question, but here goes: I see a lot of "big numbers" in physics, such as the size of the state space of all the particles in the visible Universe, and those numbers can be written down, like $10^{10,000}$, or whatever that…
Frank
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