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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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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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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Explaining Infinite Sets and The Fault in Our Stars

In watching The Fault in Our Stars I could not help but cringe at a line that flew in the face of mathematics and subsequently ruined the movie for me: "There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite…
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Types of infinity

I understand that there are different types of infinity: one can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers. Or that the infinity of the even numbers is the same as that of the…
stevenvh
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A non-mathematician’s (programmer’s) question on infinity?

I apologize for my total ignorance in the sphere of mathematics and the possibly very silly question I'm about to ask. My mathematical knowledge level is quite limited (pretty much finished with some slightly more advanced stuff then grade 12) so…
user6372
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Is infinity 'larger' than 1?

If infinity is not a number, how can it be larger than any number? A number is a position on the number line. A larger number is the position further on the number line. Infinity is not on the number line. I understand the definition of the…
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Is infinity a real number?

Is infinity a real number? If not, why not? I want some very good arguments. Thanks. $$\rightarrow\leftarrow\Huge\Huge\Huge\boldsymbol\infty$$
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Is half a pie as big as a whole pie?

I am reading an e-book called To Infinity and Beyond by Dr. Kent A Bessey. In the book the author makes the claim that Georg Cantor made a discovery "where half of a pie is as large as the whole". In talking about it, he seems to claim that because…
Daniel
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Is this conception of countable vs. uncountable infinity adequate?

I am not a mathematician, so please point out any mistakes I am making here - I am trying to grasp the concept of countable vs. uncountable infinity in a somewhat informal way and would like to know whether that conception makes sense. We can…
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Uncountable vs Countable Infinity

My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is countably infinite and the list of reals between 0…
tryashtar
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A question with infinity

I am a sophomore in high school and my math teacher did a very short lesson on infinity, here's how it went: (Try to solve each part yourself the first two are easy) Part 1 You have an inf. number of boxes each labeled like…
java
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7 Drinks - 7 Flavors - Infinite variety?

Me and three friends are trying to find the answer to a question I posed about a self-service drinks machine in our local Burger King: There is a drinks machine that has 7 varieties of drinks (coke, lemonade, orange-aid etc) and each drink has seven…
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One divided by infinity is not zero?

I know that $\frac{1}{\infty}$ is undefined. But my question is - can we say that $\frac{1}{\infty}\neq0$ ? I've got some idea how to explain that: Let's say we have a random-number generator that generates numbers in interval $(0, \infty)$. What is…
Martin Heralecký
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Does an equation containing infinity not equal 0 or infinity exist?

Does an equation containing infinity which is not equal to 0 or infinity exist? My math education stopped at poorly understanding trig so don't kill me please. OK so the question I meant to ask was if any 'operation'? using infinity as a 'factor'?…
Mazura
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What is $\frac{1}{\infty}$?

Ok. When I say "infinity," I mean an infinitely large number (such as $9999999\ldots$) So we all know the common proof for $0.999\ldots = 1$. If not, here it is: $$ \begin{align*} x &= 0.999\ldots \\ 10x &= 9.999\ldots \\ 10x-x &= 9x \\ 9.999\ldots…
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