Real Numbers form Ordered Integral Domain/Proof 1
Jump to navigation
Jump to search
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.
$\blacksquare$