# 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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### integral $\int \frac{\infty(\frac{1}{x})}{x^3}dx$ [closed]

Is anyone familiar with the following notation: $\infty \left(\frac{1}{x} \right)$? I am solving the integral $\int \frac{\infty(\frac{1}{x})}{x^3}dx$,but I have never seen this notation before. It ...
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### Cardinality of Primes in UFDs over Infinite Sets

As we know, there are infinitely-many Integer primes per, e.g , Euclid's proof. Is it also true that there are infinitely-many primes in every UFD defined over an infinite set? I tried to see if ...
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### Does Infinity grows with respect to time? [closed]

Infinity is an idea that has no endpoint and it goes on forever. Does that mean Infinity grows with respect to time?
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### Whats the error in my continuum hypothesis “proof”

First of all, I just want to say that I know my "proof" is incorrect due to the continuum hypothesis being unprovable using the standard ZFC axioms. The reason I'm posting this is because I'm self ...
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### Does$f(0) = 0, f'(x) > 0, f''(x) < 0$ imply that$f'(0)$ is equal to infinity? [closed]

As the title describes it, I am interested in the following: Suppose you have a differentiable function $f:\mathbb{R}_+ \rightarrow \mathbb{R}_+$, where $f'(x)>0, f''(x) <0$ and $f(0) = 0$. ...
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### Is the cardinality of $R^3$ greater than the cardinality of $R^2$? [duplicate]

The origin of my question is : is it possible ( at least in the abstract) to represent a portion of (physical) space on a $2D$ map, say a square map? Such a representation would require (it seems to ...
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### Why is infinity *infinity and infinity^infinity considered indeterminate?

I know that infinity is not a specific number,so we cannot apply normal algebric operations with it.But we can use the concepts of limits.So why is x^x or x*x (where x tends to infinity) indeterminate?...
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### How do people compartmentalize infinity when in the reals? [closed]

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 ...
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### Could divide by 0 be anything except plus or minus infinity

I know that division by zero is undefined, but let's put that aside for a moment. If you divide by a lower and lower amount, and approach it from a positive value, it becomes larger and larger. With ...
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### Is an uncountable infinity necessarily “bigger” than a countable infinity?

I'm not conversant in cardinality theory or set theory to formulate my question in much of a meaningful sense but I'll give it a try in hope of finding the right way to ask the question as an answer. ...
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### Prove uncountability of R using an algorithm?

Let's say I want to prove uncountability of $\mathbb{R}$ using an algorithm (I will use Python). I will consider reals $0 \le x \lt 1$ and represent the decimal development of $x$ with a generator. ...
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### $\lim_{n\to 1}(\frac{1}{1-n})=\infty$

$\lim_{n\to 1}(\frac{1}{1-n})=\infty$ When $n=1$, the equation, of course, becomes undefined, as it becomes $\frac10$ I know this can be proven since $\frac{1}{1-n}=\sum_{k=0}^{\infty}n^k$, which ...
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### How can an event with probability $0$ be possible?

Consider a dart board that is represented by a unit circle centred at the origin. Each dart lands at a singular point within the circle (or on its outer edges). Arguments that the probability of the ...
I got stuck in proving that $A=\{yn:n\in\mathbb N,y\in(1,\infty)\}$ is not bounded above? (without of course using lim)?
Let $A$ be a set of real numbers such that 𝐴⊆(1,∞) and dense in $(1,\infty)$, I would like to prove that $B= \left\{\frac{a}{(a+1)n^2}|a∈A,n∈N\right\}$ is not dense in $[1,0]$. Well I'm having some ...