Top new questions this week:

Why do people lose in chess?

Zermelo's Theorem, when applied to chess, states: "either white can force a win, or black can force a win, or both sides can force at least a draw [1]" I do not get this. How can it be proven? …

(logic) (game-theory)

asked by Brika 43 votes answered by Hagen von Eitzen 76 votes

How to create circles and or sections of a circle when the centre is inaccessible

I am doing landscaping and some times I need to create circles or parts of circles that would put the centre of the circle in the neighbours' garden, or there are other obstructions that stop me from …

(geometry) (circle) (geometric-construction)

asked by Maths Fail 34 votes answered by David 16 votes

What exactly is a number?

We've just been learning about complex numbers in class, and I don't really see why they're called numbers. Originally, a number used to be a means of counting (natural numbers). Then we extend …

(soft-question) (terminology)

asked by user164061 30 votes answered by Thomas Andrews 30 votes

Finding every $n$ such that $a_n$ is an integer

Let us define $\{a_n\}$ as $a_1=a_2=1$,$$a_{n+2}=a_{n+1}+\frac{a_n}{2}\ \ (n=1,2,\cdots).$$ Then, is the following true? If $a_n$ is an integer, then $n\le 8$. I conjectured this by using …

(sequences-and-series) (recurrence-relations)

asked by mathlove 26 votes answered by Barry Cipra 5 votes

Does there exist two non-constant polynomials $f(x),g(x)\in\mathbb Z[x]$ such that for all integers $m,n$, gcd$(f(m),g(n))=1$?

Does there exist two non-constant polynomials $f(x),g(x)\in\mathbb Z[x]$ such that for all integers $m,n$, gcd$(f(m),g(n))=1$? I think there are no such polynomials, but how to prove?

(abstract-algebra) (number-theory) (field-theory) (algebraic-number-theory)

asked by Next 18 votes answered by Qiaochu Yuan 5 votes

Why isn't the Cantor Set contradictory?

So you start with a 1-dimensional stick, remove the middle third of it, leaving 2 pieces. From each of these 2 pieces, remove the middle third. Etc. Whatever is left at the end of infinitely many …

(elementary-set-theory) (intuition)

asked by Owl 16 votes answered by Michael Hardy 13 votes

I got the answer for $\lim \limits_{x \to \infty} {\left({3x-2 \over3x+4}\right)}^{3x+1}$, but only by a mistake - how do I solve correctly?

This is what I did for: $$\lim \limits_{x \to \infty} {\left({3x-2 \over3x+4}\right)}^{3x+1}$$ Check form: $\left({\infty \over \infty}\right)^{\infty}$. Apply L'Hospital's Rule to just $\lim …

(calculus) (indeterminate-forms)

asked by Matt 14 votes answered by Brad 8 votes

Greatest hits from previous weeks:

What is the formula for calculating Profit Percentage?

Let cost price of an item be $C$, selling price be $S$. Assume the seller gets benefited. Then, Profit, $P = S - C$. Now, What is formula for calculating Profit Percent? $P \% = \dfrac{P}{C} …

(terminology) (finance)

asked by Sai Manoj Kumar Yadlapati 3 votes answered by Chris Taylor 2 votes

Surprising identities / equations

What are some surprising equations / identities that you have seen, which you would not have expected? This could be complex numbers, trigonometric identities, combinatorial results, algebraic …

(soft-question) (big-list)

asked by Calvin Lin 137 votes answered by Luis Mendo 137 votes

Can you answer these?

How prove this matrix inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$?

Question: let matrix $A,B,C\in M_{n}(C)$ is Hermitian matrix and is Positive definite matrices ,such $$A+B+C=I_{n}$$show that $$\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge …

(linear-algebra) (matrices) (inequality)

asked by china math 8 votes

How to solve this problem 4

Question $1$: Is $\frac{1}{\pi}\arccos\left(\frac{{\sqrt{2*\sqrt{2*\sqrt{2}*...n}}}}{2}\right)$ always a rational number when each$*$ is either $+$ or $-$ and $n$ may or may not be infinite? …

(trigonometry)

asked by Arkin 3 votes

Units of $\mathbb{Z}[\sqrt[4]2]$

How would one compute the units in $\mathbb{Z}[\sqrt[4]2]$? According to one source, it can be shown that the fundamental units are $1 + \sqrt[4]2$ and $1 + \sqrt{2}$, but it does not specify the …

(abstract-algebra) (number-theory) (algebraic-number-theory) (extension-field)

asked by Mayank Pandey 5 votes