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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Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?

Of course, we've all heard the colloquialism "If a bunch of monkeys pound on a typewriter, eventually one of them will write Hamlet." I have a (not very mathematically intelligent) friend who presented it as if it were a mathematical fact, which got…
Jason
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What is the result of $\infty - \infty$?

I would say $\infty - \infty=0$ because even though $\infty$ is an undetermined number, $\infty = \infty$. So $\infty-\infty=0$.
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Are there any series whose convergence is unknown?

Are there any infinite series about which we don't know whether it converges or not? Or are the convergence tests exhaustive, so that in the hands of a competent mathematician any series will eventually be shown to converge or diverge? EDIT: People…
pseudosudo
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What Does it Really Mean to Have Different Kinds of Infinities?

Can someone explain to me how there can be different kinds of infinities? I was reading "The man who loved only numbers" by Paul Hoffman and came across the concept of countable and uncountable infinities, but they're only words to me. Any help…
Allain Lalonde
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Why is $1^{\infty}$ considered to be an indeterminate form

From Wikipedia: In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by…
user9413
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Are we allowed to compare infinities?

I'm in middle school and had a question (my dad is helping me with formatting). We're learning about infinity in math class and there are a lot of problems like how it's not a number and how if you add one to infinity it doesn't change value. But…
Alice
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Why is $\infty \cdot 0$ not clearly equal to $0$?

I did a bit of math at school and it seems like an easy one - what am I missing? $$n\times m = \underbrace{n+n+\cdots +n}_{m\text{ times}}$$ $$\quad n\times 0 = \underbrace{0 + 0 + \cdots+ 0}_{n\text{ times}} = 0$$ (i.e add $0$ to $0$ as many times…
Ashley Schroder
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Is 10 closer to infinity than 1?

This may be considered a philosophical question but is the number "10" closer to infinity than the number "1"?
termsofservice
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Examples of problems that are easier in the infinite case than in the finite case.

I am looking for examples of problems that are easier in the infinite case than in the finite case. I really can't think of any good ones for now, but I'll be sure to add some when I do.
Asinomás
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Is infinity a number?

Is infinity a number? Why or why not? Some commentary: I've found that this is an incredibly simple question to ask — where I grew up, it was a popular argument starter in elementary school — but a difficult one to answer in an intelligent manner.…
Pops
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Is infinity an odd or even number?

My 6 year old wants to know if infinity is an odd or even number. His 38 year old father is keen to know too.
Kevin
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Are all infinities equal?

A friend of mine was trying to explain to me how all infinities are equal. For example, they were saying that there are the same amount of numbers between $0$–$1$ as there are between $0$–$2$. The way they explained it, you could prove that there…
Ephraim
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Koch snowflake paradox: finite area, but infinite perimeter

The Koch snowflake has finite area, but infinite perimeter, right? So if we make this snowflake have some thickness (like a cake or something), then it appears that you can fill it with paint like this ($\text{finite area} \times \text{thickness}…
ArtisanRtasin
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Why is $\omega$ the smallest $\infty$?

I am comfortable with the different sizes of infinities and Cantor's "diagonal argument" to prove that the set of all subsets of an infinite set has cardinality strictly greater than the set itself. So if we have a set $\Omega$ and $|\Omega| =…
user17762
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$\infty = -1 $ paradox

I puzzled two high school Pre-calc math teachers today with a little proof (maybe not) I found a couple years ago that infinity is equal to -1: Let x equal the geometric series: $1 + 2 + 4 + 8 + 16 \ldots$ $x = 1 + 2 + 4 + 8 + 16 \ldots$ Multiply…
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