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Real non negative numbers/Maximum/Structural properties/Exercise
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Discuss the operation
R
≥
0
×
R
≥
0
⟶
R
≥
0
,
(
x
,
y
)
⟼
max
(
x
,
y
)
,
{\displaystyle \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.
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