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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Zero and infinity

Introduction [can be skipped without loss of generality]. This question was closed and, recently, deleted, perhaps for good reason. It did have an answer with 10 upvotes, and another (mine) with 15 upvotes. So that my answer not be lost to m.se, I…
Gerry Myerson
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Infinity - a simple question

This is a simple question, and maybe stupid: Is this true: $\infty < 1000\cdot\infty$ ?
user11775
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An infinite dictionary: countably infinite or uncountably infinite?

This question concerns Ian Stewart's "Hyperwebster", an uncountable dictionary. Say a publishing company wants to publish every possible permutation (of any length) of the characters A-Z. The dictionary might look like this: A, AA, AAA, ..., AB,…
rookie
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What is infinity to the power zero

I have this notation: $$\lim_{k->\infty} k^ {1/k}$$ Is it correct to say that the output is 1, or is there some other result?
motiur
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What happens to the infinite monkey theorem when there are an infinite number of keys on the typewriter?

What happens to the infinite monkey theorem when there are an infinite number of keys on the typewriter? So what is the probability of a finite string of keys like the works of Shakespeare being typed up. Thanks for any insights.
John Marty
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Can we formally distinguish between actual and potential infinities?

Actual infinity is the idea that numbers, or some other type of mathematical object, can form an actual, completed totality; namely, a set. Hence, in the philosophy of mathematics, the abstraction of actual infinity involves the acceptance of…
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Why does it matter to approach zero from the left or right in 1/0?

I was surprised to see that 1/0 is undefined. One answer mentions that $1/0$ can be +$\infty$ or -$\infty$ depending on whether $0$ is approached by the left or the right:                     But why does this make a difference? Aren't both numbers…
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What is the result of $\infty - 1$?

I was wondering after reading "What is the result of infinity minus infinity", is there any logical result for $\infty - 1$ ?
genesis
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random thought: are some infinite sets larger than other

I was in the shower today and I just thought of this so I'm asking it. I'm sure this has been thought of before. Let's say we have two sets, the set of all even numbers and the set of all natural numbers. They are both infinite, right? But let's say…
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Are there different types of infinity?

Today in class my professor mentioned that there are different types of infinity. This confused me at first because I always thought infinity is just infinity. What are the different types of infinity?
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How can $|\mathbb{N}| = |\mathbb{Z}|$?

I have seen proofs of a bijection $f:\mathbb{N} \to \mathbb{Z}$ where $$f(n) = \begin{cases} \frac{n}{2} & n\text{ is even} \\ -\frac{n + 1}{2} & \text{else} \end{cases}$$ This shows that $\mathbb{Z}$ is countably infinite, that is, $f$ is…
Justin
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$\cdots 2222222222222222222222.0 \div \cdots 1111111111111111111111.0$

Allow us to diverge from the rules of math taught in schools and universities regarding infinities to consider this: If I have a "number" (integer-like) that goes $$\cdots2222222222222222222222.0$$ "infinitely" to the left of the decimal point and I…
cmarangu
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Infinite points on circle

Can we say that circle has infinite points? What if then I took one point out. Does it matter. And then if we took half the infinite points of the circle out of it and still can it be called circle?
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Treating $\frac{n}{0}$ as a constant?

Is there any way of treating $\frac{1}{0}$ without breaking maths? I tried just the variable $\lambda$, thinking that it would be easy to manipulate: $$\frac{2}{0} = 2\cdot\frac{1}{0} = 2\lambda$$ But I soon realised that you couldn't divide any…
user366469
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Is $\aleph_1\cdot\aleph_1=\aleph_1$?

I'm currently trying to understand the basic notions concerning infinity. I think I understand that $\aleph_0\cdot\aleph_0=\aleph_0$ but how about $\aleph_1$? Is $\aleph_1\cdot\aleph_1=\aleph_1$ i.e. is there a bijection between a line and the…
Redundant Aunt
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