Real non negative numbers/Maximum/Structural properties/Exercise

Discuss the operation

$\mathbb {R} _{\geq 0}\times \mathbb {R} _{\geq 0}\longrightarrow \mathbb {R} _{\geq 0},(x,y)\longmapsto \operatorname {max} \,(x,y),$

looking at associativity, commutativity, existence of a neutral element and existence of inverse element.

Create a solution