# Most Popular

1500 questions

**58**

votes

**3**answers

### Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$

Do you know an explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$? Using the axiom of choice, every vector space admits a norm but have you an explicit formula on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$?
A related question is: Can we proved…

Seirios

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**58**

votes

**6**answers

### Is Complex Analysis equivalent Real Analysis with $f:\mathbb R^2 \to \mathbb R^2$?

Am I correct in noticing that Complex Analysis seems to be a synonym for analysis of functions $\mathbb R^2 \to \mathbb R^2$?
If this is the case, surely all the results from complex analysis carry over to the study of these $\mathbb R^2 \to…

providence

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**58**

votes

**10**answers

### Is it an abuse of language to say "*the* integers," "*the* rational numbers," or "*the* real numbers," etc.?

I'm finding that the more math I learn, the more concepts I thought were well-defined seem to be intuitive and naive. Here I'm asking about whether it's an abuse of language to refer to "the integers," "the rational numbers," or "the real…

justin

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**58**

votes

**4**answers

### Does this Fractal Have a Name?

I was curious whether this fractal(?) is named/famous, or is it just another fractal?
I was playing with the idea of randomness with constraints and the fractal was generated as follows:
Draw a point at the center of a square.
Randomly choose any…

SilverSlash

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**58**

votes

**11**answers

### What is an operator in mathematics?

Could someone please explain the mathematical difference between an operator (not in the programming sense) and a function? Is an operator a function?

Nik

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**58**

votes

**27**answers

### Big List of Fun Math Books

To be on this list the book must satisfy the following conditions:
It doesn't require an enormous amount of background material to understand.
It must be a fun book, either in recreational math (or something close to) or in philosophy of…

RougeSegwayUser

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**58**

votes

**12**answers

### Easy way of memorizing values of sine, cosine, and tangent

My math professor recently told us that she wanted us to be able to answer $\sin\left(\frac{\pi }{2}\right)$ in our head on the snap. I know I can simply memorize the table for the test by this Friday, but I may likely forget them after the test. So…

James Smith

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**58**

votes

**1**answer

### Is $1+x+\frac{x^2}2+\dots+\frac{x^n}{n!}$ irreducible?

The polynomial $f(x)=1+x+\frac{x^2}2+\dots+\frac{x^n}{n!}$ often appears in algebra textbooks as an illustration for using derivative to test for multiple roots.
Recently, I stumbled upon Example 2.1.6 in Prasolov's book Polynomials (Springer,…

Martin Sleziak

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**58**

votes

**12**answers

### Calculating pi manually

Hypothetically you are put in math jail and the jailer says he will let you out only if you can give him 707 digits of pi. You can have a ream of paper and a couple pens, no computer, books, previous pi memorization or outside help.
What is the best…

Neil

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**58**

votes

**1**answer

### Semi-direct v.s. Direct products

What is the difference between a direct product and a semi-direct product in group theory?
Based on what I can find, difference seems only to be the nature of the groups involved, where a direct product can involve any two groups and the…

retro

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**58**

votes

**8**answers

### How can a set contain itself?

In Russell's famous paradox ("Does the set of all sets which do not contain themselves contain itself?") he obviously makes the assumption that a set can contain itself. I do not understand how this should be possible and therefore my answer to…

jimmyorpheus

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**57**

votes

**7**answers

### Why doesn't induction extend to infinity? (re: Fourier series)

While reading some things about analytic functions earlier tonight it came to my attention that Fourier series are not necessarily analytic. I used to think one could prove that they are analytic using induction
Let $P(n)$ be some statement…

David Z

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**57**

votes

**1**answer

### Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

My brother's friend gave me the following wicked integral with a beautiful result
\begin{equation}
{\Large\int_0^\infty} \frac{dx}{\sqrt{x} \bigg[x^2+\left(1+2\sqrt{2}\right)x+1\bigg]…

Anastasiya-Romanova 秀

- 18,909
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**57**

votes

**5**answers

### Self-learning mathematics - help needed!

First, I apologise for the nebulous nature of my title but I can't adequately explain myself concisely.
I am about to start an MSc in pure maths after a fairly shaky undergraduate degree. I am very passionate about maths but I have several problems…

Elliptic2005

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**57**

votes

**2**answers

### Geometry problem involving infinite number of circles

What is the sum of the areas of the grey circles? I have not made any progress so far.

Dan

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