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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Is infinity always larger than any real number?

Suppose $x$ can be any real number whatsoever. Can it be said that $x < \infty$ is true for every possible $x \in \Bbb R$? I'm asking the question in the context of infinity as defined by a left open and right unbounded interval in which $x$ is only…
Start
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What is ∞ -(∞-1)?

I have come up with two possible answers, but am unsure which is true. The first is that ∞-1 is still ∞,as ∞ is endless, and if taking away 1 made it not endless, then ∞ would not be endless either, it would just be one more then the number you got…
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Why is $\infty - \infty$ Not $0$?

∞ - 2(∞/2) There are more advanced questions on here but I often get caught up on nuances in the "basics". It seems important to clear these things up before moving on.
QWERTY_dw
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Sum question? Sum from $\infty$ to $\aleph_0$

$\sum^{\aleph_0}_{\mu=\infty}\mu=\aleph_0$? If this is true, however, then $\sum^{\aleph_0}_{\mu=0}\mu=\aleph_1$?
yayab
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Inequality operations on infinity

if $a(\infty)>b$ and $a>0$, then is it proper to write $\infty>\frac{b}{a}$?
Nothing
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Find a **bijection** between two intervals

I am struggling with this question and was hoping somebody could help me, Thanks Find a bijection between the intervals $(-1,1)$ and $(0,4)$ where $X \in R$
Emma
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What's wrong with this idea implying a contradiction in the concept of infinity?

Let be a set of something with infinite cardinality. Let ℕ be the set of natural numbers ℕ. There is a bijection f: ℕ → . They both have the same cardinality, denoted as |ℕ| = ||. Bijection means that every element of ℕ can be mapped to every…
Ariel
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mathematical operations with infinity

I suppose these are the equations with infinity that are universally considered correct: ∞ = ∞ ∞ + n = ∞ ∞ * n = ∞ n/∞ = 0 Where n can be any possible value. These equations can be rearranged to give the following results: ∞ - ∞ = 0 ∞ - ∞ = n ∞ /…
Nk07
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greater and smaller infinity?

Consider the following two expressions: $$\sum^{\infty}_{i=1}\frac{1}{i}$$ and $$\lim_{h\to90 h<90}\tan 90º$$ They both equal to infinity. I remember my teacher told me there are more real numbers than whole numbers. So $\infty>\infty$ is…
abc...
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Are there an infinite and finite amount of numbers between 0 and 1?

I saw an exchange on twitter recently, and am wondering if someone can clear this up. Are there an infinite and finite amount of numbers between 0 and 1? I thought there is an infinite amount between two numbers. I'm confused with what the person…
Ravenous
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Which one is bigger, infinity sign(∞) or aleph number?

the infinity sign(∞) is often used casually but it is very abstract concept and ill-defined... when there are 'infinite' natural numbers and aleph-zero is cardinality of a set of natural numbers.. is ∞ bigger than aleph-zero? or smaller? or it can't…
Sang
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Infinity In Math - The Nick Lim Proposal

So infinity is clearly a very strange, concept. So I have the following proposal (the nick lim proposal) which can not be solved ( at least to my current knowledge, hopefully you can shed some light ). For the following scenarios since I do not have…
Novaly
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