# 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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### why does commutativity of addition fail for infinite sums?

While discussing the sum of a particular series, $\sum\limits_{n=0}^{\infty}{\left(-1\right)}^n$ (a sum that I've heard is alleged to be equal to $\frac{1}{2}$), it was mentioned to me that addition ...
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### Countably or Uncountably Many Discontinuities

I want to know why the following function has uncountably many discontinuities: $$f(x)=\left\{\begin{array} & x^2 & x \not \in \mathbb{Q} \\ 0 & \text{otherwise} \end{array}\right .$$ ...
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### What is the limit of difference between harmonic series and natural logarithm of n+1?

I'm an undergraduate student in geology and I'm dealing with a project in math. The last question of the project gives me the harmonic series ($A_n = 1 + \frac{1}{2} + ... + \frac{1}{n}$) and this ...
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### map sum of square integers to a contiguous range of integers

Given a list $a$ of integers, $$n_{a_1}, n_{a_2}, ..., n_{a_d}$$ have $$N_a = \sum_{j=1}^d n_{a_j}^2.$$ The various $N_a$, $N_b$ etc. are integers, but are not contiguous: for example, if $d=2$, there'...
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### Are the integers closed under addition… really?

Okay so I'm a 3rd year undergraduate studying Mathematics. I've proved in group theory countless times that the integers are closed under addition. It's obvious to me that they are. However this has ...
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### Is there any mathematical or physical situations that $1+2+3+\ldots\infty=-\frac{1}{12}$ shows itself? [duplicate]

I just saw the proof that $$1+2+3+\cdots=-\frac{1}{12}$$ and my brain still hurts. I completely understood the proof and my question is NOT actually about the proof itself. At the end of the proof, ...
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### An intuitive reasoning for 1+2+3+4+5… + ∞ = -1/12? [duplicate]

I was just watching this video: http://www.youtube.com/watch?v=w-I6XTVZXww In it, a professor working at the Nottingham University( Dr. Ed Copeland I think) shows how 1+2+3+4+5....+ ∞ = -1/12 Is this ...
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### How does the sum of the series “$1 + 2 + 3 + 4 + 5 + 6\ldots$” to infinity = “$-1/12$”? [duplicate]

(I was requested to edit the question to explain why it is different that a proposed duplicate question. This seems counterproductive to do here, inside the question it self, but that is what I have ...
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### Number of Infinities in complex numbers

How many infinities would be there for complex numbers? Like there are 2 infinities ($+\infty$ and $-\infty$) for the real numbers, is there a way to prove the number of infinities in the complex ...
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### Gram-Schmidt in Hilbert space?

EDIT: After some contemplation I decided to phrase the question better to avoid trivial answers. Consider a Hilbert space with a basis $\{v_{i}\}$ where $i\in I$ an index set, which could be ...
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### Set theory, show a set is countable, homework. check my answer

I solved this question but there is something strange going on and I am unsure of myself. Would like someone to review it. We are given a total order (or linear order) $<^{*}$on group $A$ such ...
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### What good is infinity?

I am becoming increasingly convinced that Wildberger's views are, if a little bizarre, at least not hopelessly inconsistent. When I was reading the comments in the video following (MF17), somebody ...
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### Credit Given - Geometricly Modeling Infinity with 3 planes and 9 circles - Ratio of Circles

Refer to the attached diagram sketch to help visualize the equation. I am requesting help with an interesting math problem. Basically, I am diagraming infinity using three planes. These planes ...
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### Largest infinite cardinal used in a proof

I've heard before that Knuth holds the record for the largest constant used in a mathematical proof. I was wondering what is the largest cardinal ever explicitly considered in set theory. I presume ...
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### random thought: are some infinite sets larger than other [duplicate]

I was in the shower today and I just thought of this so I'm asking it. I'm sure this has been thought of before. Let's say we have two sets, the set of all even numbers and the set of all natural ...
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### How to evaluate this limit with l'hopital's rule

is it possible to use L'hopital for this or is there another method I'm missing? I have no idea how to even start this. $$\lim_{x\to \infty} \frac{(9x+1)^\frac12}{x+1}$$
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### Number of real numbers between 0 and 1 vs number of all integers [duplicate]

Let a be the number of real numbers between 0 and 1 Let b be the number of all integers. Can I say ...
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### information content of a quadratic surd

how much information is required to construct the equation: $$X^2 - 2=0 \; ?$$ suppose, in a spirit of seasonal festivity, we squander a few further bits, and pamper ourselves with the additional ...
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### Infinite compact subset of $\mathbb{Q}$

Can I find an infinite set in $(\mathbb{Q},\mathcal{T}_e|_\mathbb{Q})$ which is compact?
### if $A_n \longrightarrow \infty$ and $B_n \longrightarrow \infty$ then $(A_n+B_n) \longrightarrow \infty$ [closed]
if $A_n \longrightarrow \infty$ and $B_n \longrightarrow \infty$ then $(A_n+B_n) \longrightarrow \infty$. How do you prove it?
How would you go about calculating $$\lim_{x \to \infty} \frac{x!}{(x - k)!}$$ for some constant $k > 0$?