Proving $\max$ of $a, b$. How do I prove that $$\max{\{a, b\}} = \frac{a + b + \left | a - b \right |}{2}$$
I have no idea how to even start the proof, any idea / intuition that can get me started is greatly appreciated.
Thanks for reading my post.

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*If $a\geq b$, then $|a-b| = a-b$ and $\max\{a,b\} = a$. Now, simplify the expression you want to prove.

*If $b\geq a$, then I think you can finish the sentence.

