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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Can I prove that there are 3 times more even numbers than natural numbers by assigning each even number to a the next three natural numbers starting 0

Recently I have been thinking about infinity and more specifically, sets of an infinite size, or an infinite amount of elements in them. And I found this concept of a bijection where if each element in one infinite set can correspond to another…
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The number of even and odd natural numbers

Person A: The number of even and odd natural numbers is equal, because they alternate each time. Person B: There are far more even natural numbers. If you double an odd number, it's even. If you double an even number, it's still even. How do I best…
BmyGuest
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Understanding uncountable sets and proving that the set of non-singular intervals on the real line is countable

The problem is to prove that any set of disjoint non-overlapping intervals that contain more than a single point ("non-singular intervals) is countable. The text seems to want me to offer the following "proof:" $1$. Start with the first interval and…
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How can $\lim \limits_{t \to \infty}(1+t^2)^{p+1}$ be zero?

I am trying to integrate $$\int_1^\infty x(1+x^2)^p dx$$ I get down to $$\frac1{2(p+1)}\left(\lim \limits_{t \to \infty}(1+t^2)^{p+1}\right)-\frac1{2(p+1)}\lim \limits_{t \to \infty}2^{p+1}$$ The solution says that the next step is…
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May I Assign $\infty$ as a Value to a Variable?

Now first something that I already know; \begin{eqnarray} ∞/ ∞ = undetermined ( ≠1 ) \\ ∞- ∞ = undetermined (≠0)\\ \end{eqnarray} So basically one reason for this is that the $∞$ I assume is not as same as the $∞$ someone else will assume as $ ∞$…
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What goes wrong when we try to make a binary partition of a countable set?

Let $f$ be a function that maps an interval $[a, b]$ to some irrational number $r \in [a, b]$ that roughly splits the interval in half (e.g. both sides have at least 1/3 of the mass). Suppose we then index each $q \in \mathbb{Q} \cap [0, 1]$ with an…
GMB
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Optimal algorithm to guess any random integer without limits?

Guessing Game In Range $[1, n]$ The classical guessing game goes something like this... Our friend thinks of an integer between $1$ and $100$ (let's say they pick $42$). We try to guess that number with the fewest guesses possible: $$ 100, 3, 7,…
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Using ∞ as an algebraic term

Would it ever be possible to use ∞ as an algebraic term, putting it in equations with non infinite terms, incorporating a coefficient? Would a new type of infinity need to be defined or could aleph null work?
Mandy R
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Please help me understand this formula for Fourier analysis

I'm a programmer with a poor knowledge of math. Could anyone tell me how to read the infinity above the sigma, and the n=1 below the sigma?
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Proof that it is unsolvable whether there's an infinity between countable and uncountable?

I have recently watched a video by "Undefined Behavior", explaining countable and uncountable infinities, and showing why uncountable infinity is larger than countable infinity. He then stated that a question had been asked if there is some infinity…
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Why is this proof false?

I know this proof is false, but I don't know why. I need your help. The false proof says that it is possible to create a bijection between a subset of the rational numbers and the Power set of natural numbers. We can create orderly the subsets of…
Pedro
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Is every number compared with infinity virtually zero?

When thinking about infinity people think that a great number like googolplex or a googolplexian is closer to infinity, but infinity never ends every huge number that I can think off is closer to zero than to infinity does that make every number…
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Three kinds of infinities

In the beginning, I thought of infinity as something inaccessible. Which can't be reached. And when something can't be reached ( with 'reached' i mean can't be known) its properties were automatically considered as weird. But in the book " one two…
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Is $1/\infty=0{}$?

If $1\div0=\infty$, then $1\div(1\div0)=0$. Does this mean $1\div\infty=0$? Or is it always close to zero? Please let me know what is correct: either it's zero or always close to zero.
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Understanding the basic idea of Infinity

I'm a 10th grader looking for a way to understand infinity, I watched a bunch of videos on the topic but I just couldn't get an idea. Can someone explain the idea of infinity or rather how Cantor came up with the idea and his proof for it?