How many 10-letter words (they don't have to be actual words) can you make using 3 A's, 4 B's and the rest could be any letter from a 24-le...

I understand that equivalence relations can group elements of a set to a class that share similar properties. I think it's really cool that we can pa...

The below was inspired by this question, in which the OP was surprised that the "simple" equation $x^3 + x = 1$ could have such a "complex&...

I am presented with the following equation system $x^2 = 8+(y-z)^2$ $y^2 = 12+(z-x)^2$ $z^2 = 24+(x-y)^2$ I don't even know where to start. I am assu...

Suppose $a, b, c \in \{4, 5, \ldots, 21\}$ and satisfy $1/a + 1/b = 1/c$. Suppose also that $\gcd(b,c)=1$. Find $a, b, c$. I tried this problem and I got ...

Why can we convert a base $9$ number to a base $3$ number by simply converting each base $9$ digit into two base $3$ digits ? For example $813_9$ can be c...

Here's the thing: my textbook has an example of using the Gram Schmidt process with an integral. It is stated thus: Let $V = P(R)$ with the inner pro...

I'm s little confused about Fourier series of functions that are piecewise. Here’s an example of such a function: $$f(x) = \begin{cases} x & -\fr...

Is there a mathematical symbol that means "For every element"? I want the meaning to have similar function as an iteration, say for loop.

How to prove that $A_n$ is normal in $S_n$? Note that $A_n$ is a group of even permutations on a set of length $n$. $S_n$ is the group of all permutations...