Real Numbers form Ordered Integral Domain
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Theorem
The set of real numbers $\R$ forms an ordered integral domain under addition and multiplication: $\left({\R, +, \times}\right)$.
Proof
We have that the real numbers form a totally ordered field.
The result follows directly.
$\blacksquare$
Cop-out. Go and do the job properly, you lazy boy.
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Sources
- C.R.J. Clapham: Introduction to Abstract Algebra (1969)... (previous)... (next): $\S 2.7$: Example $9$
