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Real non negative numbers/Maximum/Structural properties/Exercise

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Discuss the operation

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \R_{\geq 0} \times \R_{\geq 0} \longrightarrow \R_{\geq 0} , (x,y) \longmapsto \operatorname{max} \, (x,y) , }

looking at associative law, commutative law, existence of a neutral element and existence of inverse element.