Real Numbers form Ordered Integral Domain/Proof 1

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Theorem

The set of real numbers $\R$ forms an ordered integral domain under addition and multiplication: $\struct {\R, +, \times, \le}$.


Proof

This follows directly from Real Numbers form Ordered Field.

The set of real numbers $\R$ forms an ordered field under addition and multiplication: $\struct {\R, +, \times, \le}$.

An ordered field is also an ordered integral domain.

$\blacksquare$