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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What is the cardinality of all frames in time?

If we divide time into individual frames, then we would get a set of infinite frames. But what is the cardinality of such a set? Since time is continuous, like the real numbers, I would expect the cardinality of all frames in time to have the same…
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May seem like a noob question: really, why can't we divide by 0?

Yes, I know, can't be answered, blah, blah, blah.... but here are a few of my theories. I know, plenty of other questions like this, but before marking this as a duplicate, consider this, my mathematical friends: We know that $ x/x = 1 $. We also…
user167906
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Incorrect proof of the infinities between 0 and 1 and 0 and 2

In reading another question (Explaining Infinite Sets and The Fault in Our Stars) it got me thinking about the way that you can prove that the number of numbers between 0 and 1 and between 0 and 2 are the same. (apologies if my terminology is a bit…
Chris
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Is infinity a real or complex quantity?

Since I was interested in maths, I have a question. Is infinity a real or complex quantity? Or it isn't real or complex?
user149881
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limits for positive and negative infinity

It says we use the l'hospital's rule, however I don't understand because the limit for positive infinity and negative infinity are different. Please help!
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Show that any interval [A, B] of the number axis is equivalent to any other interval [C, D].

I am attempting to get my head around intervals, particularly the title question as described in What is Mathematics? (Courant & Stewart). I think I am probably misunderstanding the meaning of equivalence in this context. My interpretation of the…
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Is $\infty / \infty = 1$?

Lately, my friend and I were arguing about what $\infty / \infty$ equals. My thinking was that $\infty / \infty = 1$, since no matter how high you go in the numerator, it would have to go equally as high in the denominator. My friend pointed out…
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Does infinite equal infinite?

I have a question. Let $x$ be infinite. $$2x=\infty\times2, \quad 2x=\infty$$ So actually, does $2x=x$?
Jamie
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Stuck with infinities

I have heard this "some infinities are bigger than others" . How can this be ? The context was that the cardinality of the set of integers is less than that of the cardinality of th real numbers , but how do we prove this . The more I think about…
abkds
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The primes have cardinality $\aleph_0$. How does their powerset also have cardinality $\aleph_0$?

Given that the cardinality of the naturals is the smallest infinite cardinal ( $|\mathbb{N}| = \aleph_0$ ), and the primes $\mathbb{P}$ are an infinite subset of the naturals $\mathbb{N}$, we know that that: $$|\mathbb{P}| = |\mathbb{N}| =…
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How to solve $\lim_{x\to \pm \infty} (1+\frac 1x)^x$

I have this problem: $\lim_{x\to \pm \infty} (1+\frac 1x)^x$ I understand everything except how to handle the $\pm \infty$. When I tried to solve it I reasoned like this, since both $1^\infty$ and $1^{-\infty}$ should be equal to one then the answer…
Sembfi
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Can the entire range of 2 dimensions be represented in one dimension?

If you consider the $x-y$ plane, any $(x,y)$ point exists with $x\in(-\infty, \infty)$ and $y\in( -\infty,\infty)$. Is it possible to represent any $x,y$ point in only one dimension (e.g. one number)? For example consider a discrete $8\times 8$…
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In general can we say $\infty=\infty$? Eg, $\sum_{i\in \mathbb{N}} i =\sum_{i \in \mathbb{Q}_+}i$

This might be a bit of a basic question but my current understanding is that we cannot. Still it makes me wonder if we can propose a mapping between two countable sets why not? For example why is this expression incorrect? $$\sum_{i\in \mathbb{N}} i…
EconJohn
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Is my understanding about infinity correct?

I am trying to explain how some infinities are larger than others in the easiest way possible. Here it is: Imagine a supermarket that has every food item imaginable. (But it only has food.) In fact, it has infinite varieties of food. It also has…
theknightD2
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Maximum Number in an Infinite set

Given an infinite set of random integers, is there a largest element? In other words is maximum as a concept inherently tied to finite sets?
deft_code
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