Real Numbers under Addition form Monoid

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The set of real numbers under addition $\struct {\R, +}$ forms a monoid.


Taking the monoid axioms in turn:

S0: Closure

Real Addition is Closed.


S1: Associativity

Real Addition is Associative.


S2: Identity

From Real Addition Identity is Zero, we have that the identity element of $\struct {\R, +}$ is the real number $0$.


Hence the result.