# 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.

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### Considering that there are an infinite number of numbers between two numbers, why infinite summation of equal terms cannot produce a finite result?

We know that for example the series 1/2+1/4+1/8+1/16+... does not get over 1. My reasoning of why this is possible, is that there are an infinite number of numbers or measurements between two numbers. ...
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### How should one think of infinity.

I am currently taking a first year course in mathematics and have become a bit confused when confronted with "infinity". We are covering logic and sets and I had the following homework ...
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### Infinite set such that sum of elements of every finite subset is not a power of $p$

Let $p$, be a prime number, and $S$ an infinite set of positive integers, such that all numbers from $S$ are coprime with $p$. Prove that there is an infinite subset $A\subseteq S$, such that for ...
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### Can the continuity be established at $x= 0$ for the function below?

Is this method okay to show that $f(x)=x^{-2/3}$ is discontinuous at point $x= 0$? Limit $f(x)$ as we tends from positive side of $0$, we get $+\infty$ as the value, same with $f(x)$ approached from ...
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### Hilbert's Hotel - kick everyone out

In Hilbert's Hotel scenario where an infinite number of new guests arrive, why can't we just kick everyone out and accommodate them again? Since there is already an infinite number of new guests ...
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### Closed form of equation with summation to infinity: brownian motion in a confined 1D box

I would like to implement this equation, which represent the brownian motion in one-dimension (1D) of a particle in a confined 1D box, which initial position is $x_0$ at time $t_0$ and final position ...
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### What's the difference between a dense set and an uncountable set?

I once called a dense set an uncountable set. I was told this was wrong, as the set was dense, and not uncountable. I didn't have the mathematical knowledge to find this confusing, and instead thought ...
1 vote
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Firstly, I should say that I came up with this paradox after reading of the Grimm Reapers paradox, but I’m not quite sure how this should be resolved. Nevertheless here is the problem: Suppose a lady ...
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### How to find derivative of $\sum_{n=1}^{\infty}n$

I looked at another post for finding the derivative of another sum but it had $n$ on the upper bound. But what if you had $\infty$ on the top (as in my case)? I know I could find the derivative by ...
1 vote
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### Can the entire range of 2 dimensions be represented in one dimension? [duplicate]

If you consider the x-y plane, any (x,y) point exists with x in -inf->inf and y -inf->inf. Is it possible to represent any x,y point in only one dimension (e.g. one number)? For example consider ...
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### Point at Infinity

I started to take an introduction to complex analysis course, we learned open and closed regions in the complex plane, but our professor told us that the whole complex plane is open and closed at the ...
1 vote
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### prove that $\int_0^{\infty}\frac{\{x\}\cos x}{x} dx \neq \infty$ [closed]

I can't prove that $\int_0^{\infty}\frac{\{x\}\cos x}{x} dx \neq \infty$ ({x} — fractional part x). Calculations show that this integral is approximately 0.211... It suffices for me to prove that ...
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