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Top Questions

22 votes
12 answers
3k views

Why is the empty set described as "unique" when it is a subset of every set?

20 votes
5 answers
5k views

You are given 8 fair coins and flip all of them at once. Then, you can reflip as many coins as you want. What is optimal expected number of heads?

34 votes
4 answers
3k views

Mathematical justification of this "34" array trick

34 votes
4 answers
917 views

Prove that $|z^2+1|\le 2$ implies $|z^3+3z+2|\le 6$

27 votes
1 answer
2k views

Can a non-trivial continuous function "undo" the discontinuities of another function?

13 votes
5 answers
1k views

Can there be a multiplicative linear operator for real square matrices?

9 votes
3 answers
1k views

Evaluate the integral $\int_{-\infty}^{\infty}\binom{n}{x}dx$.

10 votes
6 answers
309 views

Why is $\int_0^\infty(\frac{1}{1+x^a}-\frac{1}{1+x^b})\frac{dx}{x}=0$ for all a,b>0?

10 votes
5 answers
2k views

Can a straight line be drawn through a single node on an infinite square grid without passing through any other nodes?

16 votes
3 answers
2k views

I think I don't truly understand Cauchy's Integral theorem

17 votes
8 answers
759 views

Complex analysis book recommendations with more exercise than Ahlfors' book.

15 votes
2 answers
2k views

Which distances can I run on my treadmill?

8 votes
5 answers
2k views

A parent wants to give his horses to their three children [duplicate]

62 votes
1 answer
4k views

Is the largest root of a random polynomial more likely to be real than complex?

20 votes
3 answers
513 views

A mysterious limit: probability that a triangle captures the centre of a circle.

6 votes
3 answers
743 views

Where is the mistake in the argument in favor of the (erroneous) claim "every Dedekind cut is a rational cut"?

14 votes
5 answers
385 views

Is there a dense subset of the rationals (between 0 and 1) that doesn't include its midpoints?

7 votes
5 answers
1k views

Why is construction required in geometry?

9 votes
3 answers
1k views

Proof explanation of result 5.11 in Linear Algebra Done Right, Sheldon Axler

12 votes
3 answers
3k views

How many rolls are sufficient to ensure, with probability 99%, that the sum is greater than 100?

16 votes
2 answers
948 views

Crazy integral with nested radicals and inverse sines

8 votes
5 answers
902 views

Evaluating a rational function integral in a quick way

8 votes
3 answers
2k views

Is it true that |X| vanishes at infinity, then X is integrable?

14 votes
3 answers
2k views

A seemingly contradictory function - where's the issue?

7 votes
5 answers
1k views

Finding the area of a quadrilateral in this picture

8 votes
2 answers
733 views

Algebra Math Olympiad Question

7 votes
4 answers
1k views

Disproving surjectivity of $f : \Bbb Z \times \Bbb Z \rightarrow \Bbb Z$, $f(u,v) = 3u + 6v$

12 votes
3 answers
2k views

Parabola as a limit of sequence of function $f(x)=\sum_{k=-n}^{n} |x+k|$

9 votes
2 answers
707 views

What does it mean to say that a linear transformation *is* the change of basis matrix?

14 votes
3 answers
2k views

43 cookies are randomly given to 10 children. What's the probability each child receives at least 2 cookies?

6 votes
3 answers
1k views

Given 4 red, 3 white and 5 black balls. Picking balls one by one without replacement, find the chance that red balls are exhausted first.

2 votes
4 answers
699 views

Why does set-theoretic union and intersection operate on reverse logic?

3 votes
5 answers
676 views

Does a finite intersection (or union) generalise to an arbitrary one?

9 votes
3 answers
638 views

How can I evaluate the Gaussian Integral using power series?

4 votes
5 answers
615 views

Discriminant formula - do the coefficients include their signs?

8 votes
2 answers
693 views

Question regarding multiplication table of group of odd order.

5 votes
2 answers
611 views

Population size change with equally probable growth and decline

6 votes
3 answers
567 views

Continuous addition and multiplication on Euclidean space (dimension > 2) making it into a field?

8 votes
2 answers
930 views

Number of ways a chess king can move from a1 to h8

12 votes
1 answer
727 views

Taking the inverse (not the reciprocal) of both sides of an inequality

4 votes
4 answers
554 views

Find $ \lim_{x\to+\infty} \cos^{2}(\sqrt{x+4})-\cos^{2}(\sqrt{x+1}) $

4 votes
4 answers
420 views

Looking for alternative proofs of this statement about angles

3 votes
2 answers
450 views

How many seven-digit numbers have seven distinct nonzero digits that appear in increasing order from left to right?

14 votes
5 answers
531 views

Is every triangle a difference of two squares?

8 votes
5 answers
637 views

Expected Number of Flips and Probability in a Coin Toss Experiment

14 votes
3 answers
597 views

What is the least number of circles with radius $r$ is required to cover a circumference of a circle with radius $R>r$?

2 votes
2 answers
362 views

MIT Bee Qualifiying Exam 2024, Question $20$: $\displaystyle \int _1^3 \dfrac{x+\dfrac{x+\dots}{1+\dots}}{1+\dfrac{x+\dots}{1+\dots}}\,dx$

11 votes
4 answers
348 views

How to evaluate $\int_{-\infty}^\infty \frac{x-2}{(x^2+x+4)\sqrt{x^2+2x+4}}dx $


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