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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Infinite chessboard question

Suppose there is a species of aliens called cyborgs. There is an infinite chessboard in their homeland. There is 1 cyborg on every square. If cyborgs can jump infinitely far, or jump and land on their same square, is it possible to get 2 cyborgs on…
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Infinite expansion of non-linear expressions with 3 or more variables

I just realised that if we expand any of the non-linear expression with power of 3 or more we can't stop expanding them until we are dead. So for example: Expansion: $(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac$ Grouping: $(a+b+c)^2 = \textbf{(a +…
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About the order of infinity of $\Re^n$

I would like to ask a question about the order of infinity of the $n$-dimensional space $\mathbb{R}^n$. I am not sure whether I use the appropriate notation/mathematical language or not - please correct me, if necessary. If I am not confused,…
nullgeppetto
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Does infinite time = time with no end = never?

Say an object is to travel from point A to point B, a finite distance of 2 meters. Say the object travels at 1m/s. After 1 meter the speed of the object is halved. After another half of the previous distance the speed is halved again, and so on. So…
RussW
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Is one infinity bigger than another?

Given a 2d plane. With a coordinate system, you can identify an infinite amount of points. That is, the set S of points that lie on the plane has an infinite number of elements. Now say you only consider the first quadrant of the plane (taking the…
Saksham
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Sum of infinitely cut lines

Suppose we split a line which length is $1$ in half. Then we get the $2$ lines which length is $1/2$ . Divide these two lines equally in half. Suppose we repeat this process infinitely. The length of lines can be calculated $\lim_{N \to…
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How to understand the counterintuitive fact that you can calculate an infinite geometric series?

If you add and multiply infinitely, it keeps increasing, doesn't it? And yet we have this formula, if $0
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Is 1 + infinity > infinity?

Ok so I'm arguing with this one person that says that $1 + \infty > \infty$ is true, and I disagree. But I can't disprove their points. My argument is that if $1 + \infty > \infty$ then there exists a number greater than $\infty$, disproving the…
Thezi
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Infinite division of an infinitely large set

What happens if one divides an infinitely large set into two equal parts - or eliminates half the members of the set - an infinite number of times? Two intuitions: After each elimination, the remaining set is still infinitely large, thus even an…
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Why does $\sum_{i=0}^{\infty}(0)$ not equal to $x + \sum_{i=1}^{\infty} (-x + x)$ where $x \in \mathbb{R}$?

I feel like something is wrong here in my logic but why do these two equations not equal each other? Equation 1: $\sum_{i=0}^{\infty}(0)$ Steps to equation 2: $0 = x - x$ where $x \in \mathbb{R}$ therefore, $\sum_{i=0}^{\infty}(x - x)$ which could…
RohanP
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Is a real interval an example of actual infinity

Actual infinity, unlike potential infinity, is one interpretation of infinity where there is an end, of which we have no idea, say counting numbers (1,2,3,4,... it keeps going). I have read about Cantor's ideas of countable and uncountable sets and…
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Can 0 divided by 0 equal Infinity

Can $1 \div 0$ equal $\infty$? My evidence is: $1 \div 0.1 = 0.1$ $1 \div 10^{-2} = 100$ $1 \div 10^{-3} = 1000$ $1 \div 10^{-4} = 10^4$ $1 \div 10^{10^{3}} = 10^{1000}$ $1 \div 0 = \infty$ Can $1 \div 0$ equal $\infty$, or does it have to be…
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Is infinity and recursion linked?

noob question, from a programmer with a light background in mathematics. I was thinking about how one would definite infinity, and came across a thought: how could one define infinity? One thought was: "the number one bigger than the biggest number…
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Can we count past $ \infty $?

Let's say, $ \infty $ is not the biggest number, in fact, there is something bigger, somewhere. We want to try and count past $ \infty $, because it is not really an ordinal one, but a definition of something uncountable or too big to even…
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Is it possible to have an infinitely repeating whole number

So I would like to know whether I could have a repeating whole number, such as 9999... repeating or if that's a mathematical fallacy that breaks things. I don't really want to know if it would be natural or not (I assume not), I'm just wondering if…