Tagged Questions

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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Division of segments into infinitely many parts.

Let AB and CD be two segments, so that the length of AB is 1, and the length of CD is 2. If we divide AB and CD in infinitely many parts, how "long" would those parts be? I'm particularly interested ...
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When adding or subtracting two infinite sums, why is there no issue with “staggering” or arbitrarily manipulating the “alignment” of terms?

I was watching Ramanujan: Making sense of 1+2+3+... = -1/12, where the presenter writes: (I tried to write this out in $\LaTeX$ but couldn't figure out how to do multi-column alignment without ...
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Summing Over Uncountable Index Sets

In answering the question Why do we classify infinities in so many symbols and ideas?, William's answer asserted that summing over an uncountable index set necessarily results in an infinite sum. I am ...
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Does the graph $y=\sin(x)\times\sin(x^{-2 })$ cross the $x$ axis an infinite amount of times in a finite interval?

Vsauce made a video recently on counting past infinity, and he represented the set of natural numbers to infinity with a set of lines, where each successive line is a smaller distance away from the ...
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What is infinity to the zeroth power? [closed]

I am not happy with the answers posted to similar questions. For example, in: What is infinity to the power zero the accepted answer is 1, which is definitely wrong. I think the answer is any non-...
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Can I subtract infinity from infinity?

I was stuck when solving a problem on limits. It was like----> $\lim_{x\to\infty} (x-x)$. What should I do now?
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Why can't we keep adding axioms forever?

Let F be a formal system falling prey to Gödel's incompleteness theorems, implyng there is a true but unprovable statement, call it $G_1$. Of course, adding $G_1$ to the axioms of F doesn't solve the ...
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Definition of limit as $x\rightarrow \infty$

Every time i get confused with the definition of $\lim_{x\rightarrow \infty}f(x)=L$. I could not find a reference that will give the definition. I am trying to write what i understood. See if this is ...
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Show that if |f(x)| converges in infinity, so is f(x).

I think that in a I should compare the function |f(x) - f(x) and 2|f(x)| but I am not sure how i would do that. Also, I am not sure how i should duduce what i want to deduce in b after i find a.
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Product of all real numbers in a given interval $[n,m]$

READ-ME I have now what I can call for myself answers to all my problems and subquestions proposed in this post, thus I accepted Strings answer as the answer to this question since it was of most ...
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How to compute log likelihood for impossible events?

I am defining a set $\mathbf{Z} = [p,q,r,s]$ such that $Pr(p)+Pr(q)+Pr(r)+Pr(s)=1$. Likelihoods are defined as follows \begin{align} \lambda_p&=\log \frac{Pr(x=p)}{Pr(x=s)}, \hspace{2mm} \...
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Is $\sum_{n=0}^\infty (a \cdot r^n)$ equivalent to $\lim_{n \to \infty}\sum_{k=0}^n (a \cdot r^k)$?

In other words, when writing down an infinite sum, are we always implying that it's actually the limit of that series as the number of terms approaches infinity, or is there some subtle difference?
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Is this line of reasoning correct/valid?

I'm only in the second month of my first calculus course, so I'm not sure how much sense this question will make. I'll give it a try anyways though. Let's say you have the sum of an infinite series ...
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How can one prove this generalization?

In two dimensional space, the length of a vector is $$\sqrt{x^2+y^2}$$ In three dimensional space, the length of a vector is $$\sqrt{x^2+y^2+z^2}$$ How can one prove that in n th dimensional space ...
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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 ...
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$\infty$ and $-\infty$ are to $\aleph_0$ / $\beth_0$ as “what” is to $\beth_1$?

So, I recently asked a question about whether $\beth_1$ had a negative, and I was promptly reprimanded because I confused $\aleph_0$ with $\infty$. Therefore, to help me understand the concepts ...
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