User WimC

131 votes

Accepted

Why is $\frac{987654321}{123456789} = 8.0000000729?!$

arithmetic rational-numbers

answered May 19, 2013 at 8:35

77 votes

Accepted

Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?

real-analysis elementary-set-theory

answered Oct 2, 2013 at 18:18

60 votes

Prove that $\log(n) = O(\sqrt{n})$

asymptotics

answered May 16, 2012 at 16:36

59 votes

Can every proof by contradiction also be shown without contradiction?

logic proof-writing propositional-calculus proof-theory

answered Nov 24, 2012 at 16:06

35 votes

If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.

elementary-number-theory modular-arithmetic divisibility factorial

answered Jun 30, 2012 at 10:13

35 votes

Making 400k random choices from 400k samples seems to always end up with 63% distinct choices, why?

probability random balls-in-bins

answered Jul 21, 2014 at 16:14

33 votes

How many positive integers $< 1{,}000{,}000$ contain the digit $2$?

combinatorics

answered Feb 9, 2014 at 17:53

28 votes

Accepted

Please prove that the Probability Mass Function (in Binomial Distribution) is less than 1.

probability

answered Dec 8, 2012 at 6:38

27 votes

Why does $ \int_0^1 \lceil { x\sin({1 \over x})} \rceil \,dx = 1 - \frac{\log(4)}{2\pi} $?

calculus integration

answered Jul 29, 2015 at 12:26

23 votes

Accepted

Proving that $\sin x \ge \frac{x}{x+1}$

calculus real-analysis trigonometry inequality

answered Nov 6, 2012 at 20:30

21 votes

Mapping half-plane to unit disk?

complex-analysis

answered Feb 29, 2012 at 8:55

21 votes

Accepted

How to efficiently generate five numbers that add to one?

puzzle random

answered Jun 16, 2013 at 17:30

20 votes

Integral $\int_{0}^{1}\ln x \, dx$

integration limits

answered Dec 25, 2012 at 9:53

18 votes

Accepted

Proof that a function with a countable set of discontinuities is Riemann integrable without the notion of measure

calculus real-analysis integration

answered Dec 23, 2012 at 21:27

18 votes

Calculate sum of $\sum_{n=1}^{\infty}(-1)^n\frac{\ln n}{n}$

real-analysis

answered Jan 10, 2013 at 22:07

17 votes

Accepted

Limit of complex function

limits complex-numbers

answered Nov 24, 2012 at 11:19

17 votes

Accepted

Find $\sum_{n=1}^\infty {\frac {f(n)} {n(n+1)}}$ where $f(n)$ is the number of $1$s in $n$'s binary expansion

sequences-and-series binary

answered Mar 16, 2014 at 9:48

16 votes

Accepted

What's the most elementary way to solve this trigonometric problem?

trigonometry triangles

answered Jan 3, 2021 at 7:48

16 votes

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101 positive integers placed on a circle

combinatorics pigeonhole-principle

answered Jan 20, 2013 at 10:54

15 votes

Proving that $\lim_{z \to 0} \frac{\bar{z}}{z}$ does not exist

complex-analysis

answered Nov 4, 2012 at 18:13

15 votes

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Disproving an "almost true" trigonometric identity

trigonometry

answered Aug 26, 2014 at 5:13

15 votes

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How do we check if a polynomial is a perfect square?

polynomials

answered Sep 5, 2014 at 18:50

14 votes

Explaining a Fibonacci

fibonacci-numbers

answered Oct 28, 2012 at 19:45

14 votes

A bound on a sum of five sines

calculus

answered Apr 29, 2013 at 7:34

13 votes

Without using approximation, prove that $ \ln(4)<\sqrt{2}$.

inequality

answered Jan 12 at 21:26

12 votes

Accepted

How can I evaluate this improper integral?

calculus integration improper-integrals

answered Jan 1, 2013 at 18:22

12 votes

Are there any simple ways to see that $e^z-z=0$ has infinitely many solutions?

complex-analysis

answered Apr 28, 2012 at 10:14

12 votes

Accepted

Do there exist equations that cannot be solved in $\mathbb{C}$, but can be solved in $\mathbb{H}$?

complex-numbers quaternions

answered May 13, 2014 at 14:11

12 votes

Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$

polynomials

answered Jun 7, 2014 at 7:24

10 votes

Proof of a simple property of real, constant functions.

real-analysis functions

answered Feb 26, 2012 at 18:56

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666 Answers

Why is $\frac{987654321}{123456789} = 8.0000000729?!$

Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?

Prove that $\log(n) = O(\sqrt{n})$

Can every proof by contradiction also be shown without contradiction?

If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.

Making 400k random choices from 400k samples seems to always end up with 63% distinct choices, why?

How many positive integers $< 1{,}000{,}000$ contain the digit $2$?

Please prove that the Probability Mass Function (in Binomial Distribution) is less than 1.

Why does $ \int_0^1 \lceil { x\sin({1 \over x})} \rceil \,dx = 1 - \frac{\log(4)}{2\pi} $?

Proving that $\sin x \ge \frac{x}{x+1}$

Mapping half-plane to unit disk?

How to efficiently generate five numbers that add to one?

Integral $\int_{0}^{1}\ln x \, dx$

Proof that a function with a countable set of discontinuities is Riemann integrable without the notion of measure

Calculate sum of $\sum_{n=1}^{\infty}(-1)^n\frac{\ln n}{n}$

Limit of complex function

Find $\sum_{n=1}^\infty {\frac {f(n)} {n(n+1)}}$ where $f(n)$ is the number of $1$s in $n$'s binary expansion

What's the most elementary way to solve this trigonometric problem?

101 positive integers placed on a circle

Proving that $\lim_{z \to 0} \frac{\bar{z}}{z}$ does not exist

Disproving an "almost true" trigonometric identity

How do we check if a polynomial is a perfect square?

Explaining a Fibonacci

A bound on a sum of five sines

Without using approximation, prove that $ \ln(4)<\sqrt{2}$.

How can I evaluate this improper integral?

Are there any simple ways to see that $e^z-z=0$ has infinitely many solutions?

Do there exist equations that cannot be solved in $\mathbb{C}$, but can be solved in $\mathbb{H}$?

Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$

Proof of a simple property of real, constant functions.