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Shinrin-Yoku
  • Member for 2 years, 3 months
  • Last seen this week
798 votes
49 answers
125k views

Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)

578 votes
21 answers
90k views

Mathematical difference between white and black notes in a piano

  • 5,667
539 votes
0 answers
19k views

Does there exist a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?

  • 69.4k
445 votes
23 answers
85k views

Proofs that every mathematician should know. [closed]

  • 1,107
370 votes
15 answers
25k views

Can every proof by contradiction also be shown without contradiction?

  • 9,393
344 votes
7 answers
46k views

How can you prove that a function has no closed form integral?

275 votes
1 answer
25k views

How discontinuous can a derivative be?

265 votes
6 answers
144k views

What is the practical difference between a differential and a derivative?

  • 2,651
252 votes
9 answers
30k views

Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$

  • 43.3k
240 votes
28 answers
33k views

Your favourite application of the Baire Category Theorem

237 votes
11 answers
179k views

What is the result of $\infty - \infty$?

  • 3,279
216 votes
4 answers
36k views

How do I convince someone that $1+1=2$ may not necessarily be true?

  • 2,179
209 votes
6 answers
67k views

When can you switch the order of limits?

  • 9,126
177 votes
4 answers
63k views

Overview of basic results about images and preimages

174 votes
17 answers
156k views

How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?

  • 7,710
173 votes
2 answers
98k views

Discontinuous derivative. [duplicate]

  • 1,847
170 votes
10 answers
10k views

How far can one get in analysis without leaving $\mathbb{Q}$?

  • 26.1k
152 votes
5 answers
23k views

What is the Riemann-Zeta function?

149 votes
28 answers
21k views

Simple theorems that are instances of deep mathematics

148 votes
2 answers
43k views

Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$

  • 31.5k
132 votes
1 answer
25k views

Overview of basic facts about Cauchy functional equation

131 votes
16 answers
17k views

Why did mathematicians take Russell's paradox seriously?

  • 3,221
130 votes
18 answers
12k views

Division by zero

  • 1,527
127 votes
9 answers
23k views

Prove that $C e^x$ is the only set of functions for which $f(x) = f'(x)$

121 votes
5 answers
22k views

Construction of a Borel set with positive but not full measure in each interval

  • 8,003
117 votes
8 answers
13k views

Are the "proofs by contradiction" weaker than other proofs?

  • 6,072
115 votes
1 answer
4k views

Convergence of $\sum_{n=1}^{\infty} \frac{\sin(n!)}{n}$

112 votes
2 answers
7k views

What makes a theorem "fundamental"?

  • 11.1k
111 votes
12 answers
13k views

Why are mathematical proofs that rely on computers controversial?

  • 4,004
111 votes
12 answers
17k views

Why can't calculus be done on the rational numbers?

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