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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Sizes of infinities

How is it that some infinities are bigger than other infinities and also If I have an infinite amount of apples and an infinite amount of planet earths then which will have the greater mass? (My intuition is leaning more towards obviously planet…
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How can we think about infinity?

Consider the following abstraction. We have a skyscraper with an infinite number of floors. The first floor contains the first type of infinity $\aleph_0$. So I guess finite numbers can live in the basement (or nowhere if we just talk about…
pushkin
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Probability of getting black or white

If I have a bag of black and white marbles, say 10 black and 10 white, I have a 50% chance of either getting black or white. What if the bag were infinite? Can one talk about probability when dealing with infinite sets? I ask this question because…
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Comparing Infinities

Is it ever possible to say that $\infty = \infty$? For example, does the number of odd numbers ($\infty$) equal the number of even numbers ($\infty$)? Does does the number of odd numbers ($\infty$) even equal the number of odd numbers ($\infty$)?…
Dodo
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Infinite or unknown?

If you have $0$ clients on Monday, and $5$ clients on Tuesday, how many times have the number of clients you had grown from Monday to Tuesday? $A$ - Infinite times $B$ - Unknown $C$ - Undefined
user893730
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The real projective line and $1/\infty$

so I came up with this idea: the real projective line defines that $\infty = - \infty$. What if I divide any value $x$ (not equal to $\infty$) by infinity? Would that be 0? or "something" between $x/\infty$ and $x/-\infty$? Would be very…
A_K
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Are there any certainties of properties of infinity?

I have been considering the properties of infinity and applications to various areas of maths and was hoping to get some opinions of more seasoned mathematicians than myself. One geometric representation of infinity could be that of a vertical line…
IIJHFII
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Problems with x/∞

If $\dfrac {x} {\infty }=0,$ where $x$ is a finite number, than wouldn't $0\cdot \infty $ be equal to any number? Making this not work?
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Infinity figure of eight

I'm trying to build some jewellery in a 3D cad package. I found this: The function that draws a figure eight But I don't understand the equation (I only got to A' level :) Is there a way of calculating cartesian [x, y] positions from this? Any help…
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Reversing a number of infinitely many digits

Lets say we have a function that gets as input a real number and returns its reverse e.g. 123.12 -> 21.321 So what happens when the input is a number α that has infinitely many digits. Does then reverse(α) exist as a number? Is this number well…
Lan Pac
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Convention on infinity comparision

What's the difference between $-\infty \leq a \leq \infty$ and $-\infty < a < \infty$ conceptually or otherwise. It doesn't really affect the solution to the solution of this problem I'm working out( I hope) but the solution states $\leq$ and I…
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Discount in Infinity

I fully understand that $0.9999...$ mathematically will equal 1.0 exactly as the repeating decimal continues infinitely. This would be contrary to conventional logic where such a fraction is considered approximately 1.0 and not exactly 1.0. Here, of…
Jon
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If $0{.}9\ldots$ is $1$, what does that make $0{.}3\ldots$?

So I recently learned that $0{.}9$ repeating is equal to $1$: $$ x = 0{.}9\ldots\\ 10x = 9{.}9\ldots\\ 9x = 10x - x = 9{.}9\ldots - 0{.}9\ldots = 9\\ x = 9x/9 = 9/9 = 1\\ x = 1 $$ Or a simpler proof: $$ x = 1/3 = 0{.}3\ldots\\ 3x = 3/3 =…
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Proving that if a set $A$ is infinite then necessarily $|A|\geq|\mathbb{N}|$

A set $A$ is set to be infinite if it is not finite, i.e. if there exists no $n\in\mathbb{N}$ such that $|A|=n$, meaning there exists a bijection $A\leftrightarrow\{1,\dotsc,n\}$. How do I prove that for any such set there necessarily exists an…
MickG
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Why does Infinity x Zero not Equal One?

Why does Zero Times Infinity not equal One ($0 \times \infty \neq 1$)? If Infinity = $\infty$ and Zero = $\frac{1}{\infty}$ Then Zero Times Infinity = $0 \times \infty = \frac{1}{\infty} \times \infty$ which is equal to '$1$'? What Am I doing wrong?
zordman
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