Math Test

This is an example of a paradox: $$R := \{x \mid x \not\in x\}.$$ They are not good.

Here is some inline math: $\sum_{k = 1}^{\infty} \frac{1}{k}$.

$n$-th root irrationality theorem

For any positive integer $n > 2$, $\sqrt[n]{2}$ is irrational.

Proof: Assume $\sqrt[n]{2}$ is rational. Then $2 = \frac{p}{q}$, and thus $q^n + q^n = p^n$. This contradicts Fermat's Last Theorem, so the $n$-th root of two is irrational.