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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How can incremental fees be infinity for the majority of fund managers who don't beat the market?

Kindly see the emboldened sentence below. Is it hyperbole? How can fund managers charge infinity as a fee?!!?!       But even this recalculation substantially understates the real cost of active beat-the-market investment manage-ment. Here's why:…
user53259
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Infinity and Negative Infinity Logical Query

If infiniti is the highest theoretical number then what is the opposite of it? At first glance one might think 0 but that is not true. Research (aka a quick google search) has shown me that the opposite of infinity is called infinitesimal(sorry if I…
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How do people compartmentalize infinity when in the reals?

We see the common questions in math going through highschool. 1^infinity, undefined, why? Because infinity isn't defined in the reals? So we reorganize the question to include a limit, but we still use the symbol infinity in the limit definition.…
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Are some infinities really bigger than others?

I'm not a mathematician, but I recently read a thread about how some infinities are bigger than others. The argument put forward was that of mapping pairs of numbers from reals to naturals. There is also the argument of: How many numbers are there…
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What is the correct answer of 1/0 or 1÷0 and why?

Few days ago, i was attending lecture of Introduction to Computers (ITC) in my University and there was one question. ** What is 1/0 or 1(divide-by) 0. ** I checked it on my phone and it says 1/0 is infinite and my Professor said that it is not…
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Random selection in an infinite set

If I had an infinite number of sticks and (somehow) painted sticks #1,4,7,10.. in red and then painted sticks #2,3,5,6,8,9... in blue. Then I picked a stick at random, do I have more chance of picking a blue stick or is the probability the same…
Gueda
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Can one infinity be greater than other?

Both these limits tend to infinity but it is obvious to say that $$\lim_{x \to 0}\frac{2}{x} \gt \lim_{x \to 0}\frac{1}{x}$$ as at any point it is true, if not what about these one $$\lim_{x \to 0}\frac{1}{x^2} \gt \lim_{x \to…
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What is ($\sqrt{-1}$ or $i$) $\cdot$ $\infty$

Let: $x=\infty\cdot i$ $y = \frac{\infty}{i}$ Find $\ x\ $and$\ y.\ $ Does this even make sense? Would $x$ just be $\sqrt{-\infty}$? I'm confused as to what's going on here.
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Divide by zero on Android

Various calculators give various values when you divide by zero.Windows calculator says you that that's impossible, but Android ones give 0 or infinity.Can anyone explain why?
JetFly
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If $0.999\cdots = 1$ Then Does $\frac{1}{10^\infty} = 0$?

Recently I stumbled across a, to me, rather strange idea. I was messing around with the proof of $0.999... = 1$, when I figured that what $0.999...$ means is that those are all nines. That way I came upon a weird idea. Say $a = 0.999...$, then $a =…
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difficult in understanding the concept of underflow in deep learning

I'm currently reading the deep learning book written by Ian Goodfellow, In chapter 4, there is a paragraph about underflow "One example of a function that must be stabilized against underflow and overflow is the softmax function. The softmax…
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Is $ \infty^{\infty} = \aleph_0$?

Note: I read something about this on the internet somewhere once, my logic could be 100% flawed. Is $(\aleph_0)^{\infty} = \infty^{\infty}$? Suppose the number $\infty^{\infty}$. Assuming $\infty$ in this sense has a cardinality of $\aleph_0$,…
Travis
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Is $\infty+ i\times \infty$: $\tilde{\infty}$?

Mathematica would leave $\infty+i*\infty$ there, no more simplification. Before I ask the question, there are number of assumptions I have. If any of them is not right, please point it out. Thank you! I assume what Mathematica means when displaying…
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If infinity is never reached, then how does one assume that s/he approach infinity?

Many times I have read or heard that we can tell that a value approaches infinity. Yet, if infinity is not an exact value, but a general idea, how can it ever be approached? Any number that you think approaches infinity can just have one added to…
Tim K
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infinity between two points on a line

I remember from school that the number of points on a section of a line is infinite. On the other hand, when you reach the number two in a number sequence, that is a number and how big the number is, it will never become infinite. But on the line…
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