TITLE: Why should we prove obvious things?
QUESTION [73 upvotes]: Obviously, there are obvious things in mathematics. Why we should prove them?

Prove that $\lim\limits_{n\to\infty}\dfrac{1}{n}=0$?
Prove that $f(x)=x$ is continuous on $\mathbb{R}$?
$\dotsc$

Just to list few examples.

REPLY [2 votes]: If it's obvious then the proof should be trivial and pose no inconvenience. If you find it difficult to prove then perhaps it's not so obvious.