Real Numbers under Subtraction do not form Semigroup

Theorem

The set of real numbers under subtraction $\struct {\R, -}$ does not form a semigroup.

Proof

We have that Subtraction on Numbers is Not Associative.

Hence $\struct {\R, -}$ is not a semigroup by definition.

$\blacksquare$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 4.4$. Gruppoids, semigroups and groups: Example $77$