Extended Real Numbers under Multiplication form Commutative Monoid
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Theorem
Denote with $\overline \R$ the extended real numbers.
Denote with $\cdot_{\overline \R}$ the extended real multiplication.
The algebraic structure $\struct {\overline \R, \cdot_{\overline \R} }$ is a commutative monoid.
Proof
By Extended Real Numbers under Multiplication form Monoid, $\struct {\overline \R, \cdot_{\overline \R} }$ is a monoid.
By Extended Real Multiplication is Commutative, $\cdot_{\overline \R}$ is commutative.
Hence $\struct {\overline \R, \cdot_{\overline \R} }$ is a commutative monoid.
$\blacksquare$