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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Does $\frac {1}{∞} = 0$?

Actually , I am not believing that $\frac {1}{∞} = \frac{0}{1}$ because simply $0 ≠ 1$ (we get this if we multiple numerator by denominator) , In the other hand it is very very very small , So I am confused
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Is $\infty$ undefined?

I am confused at $\infty$ in a lot of ways. First, we sometimes say that ${1\over 0}=\infty$. That gives us these confusing calculations.$${1\over0}=\infty$$ $$1=0*\infty$$ $$2=(0*2)*\infty$$ $$2=0*\infty$$ $$1=2$$ But certainly, this is not true.…
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Isn’t dividing by 0 similar to multiplying by infinity?

A commonly cited proof for being unable to divide by zero is as such: 0 = 0 * 1 0 = 0 * 2 0 * 1 = 0 * 2 (divide both sides by 0) 1 = 2 That’s obviously unacceptable, but consider the following (assume ∞ is infinitely large and 0 is infinitely…
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Which set does $\infty$ refer to?

The extended real number line is sometimes written as $\mathbb{R} \cup \{+\infty\} \cup \{-\infty\}$. In ZFC, this would imply that $+\infty$ is some set. In other words, the string $+\infty$ is an identifier for a particular set. So... which set…
extremeaxe5
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Is the infinite content in different ways?

If between $ 1 $ and $ 2 $ there are infinite numbers, then the infinity is contained between $ 1 $ and $ 2 $? And also, the infinite of the reals, is greater than, that of the natural ones? Since the real contains the natural, integers, etc.…
ESCM
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A question about infinity

If I take infinity and subract one from it,then I'll get infinity, but what if i take that result and subtract one again and I repeat that process an infinite number of times. Shouldn't I get infinity. but isn't that equal to $\infty-\infty $ which…
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Are these formulations correct?

Give rigorous formulations of the following statements. i) $f(x) \to \infty $ for $x \to \infty $ ii) $f(x) \to -\infty $ for x $ \to \infty $ iii) $f(x) \to \infty $ for $x \to -\infty $ iv) $f(x) \to -\infty $ for $x \to -\infty $ v) $f(x) \to…
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On algebraic operations involving $-\infty$ and $+\infty$

$-\infty$ and $+\infty$ are two mathematical objects that we attach to the real number system to extend it. These objects are governed by a set of properties. However, I'm confused on a few points. Any clarification on these points would be greatly…
user405743
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Intuitive explanation of different types of "infinity"

I have been taught in some computer science theoretic courses that two types of infinities exist: dense and countable, e.g. dense (uncountable) : real numbers, countable: integers. And that therefore dense "sort of" > countable... I would be…
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points on a circle ARE countable???

I always thought that the points on a circle would be uncountable, like the real numbers between 0 and 1. But I read or saw something that made me wonder. It said you could form a one to one pairing between the integers and the points on a circle of…
bazbsg
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What is the chance of an infinitesimally small chance happening over infinite tries?

If you have an infinitesimal chance of succeeding at something, but you do it an infinite amount of times, what is the probability that you succeed at least once?
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Value of an infinite series

How can we find the value of $(1+x)(1-x+x^2-x^3+x^4....... \textrm{infinity})$. I think it will be 1 but not too sure of it. I think all the terms will get cancelled only 1 remains but how to show it?
Suprabha
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How $\infty=\infty$.

If we contruct two strainght lines as shown: Then join them such that to complete a triangle. It is taught that we can find infinity points on straight line. So there are infinity points on $DE$ and $BC$. If we will join $A$ with $BC$ as shown: We…
mnulb
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Positive continuous function with non-zero limits in $\pm\infty$ whose integral over $\mathbb{R}$ is $1$?

Is it possible to create a positive continuous function with non-zero limits in $+\infty$ and $-\infty$ whose integral over $\mathbb{R}$ is $1$? I am studying the probability density functions and one of the conditions mentioned are that limits of…
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infinity understanding problem?

between 0 meter -> 1 meter there are 100 cm. but each cm has infinite numbers : for example between 0..1 cm there are : 0.000000000001 .. 0.00000000000111 .. 0.000000000001111111 and more numbers and combinations... .. …