Real Numbers form Integral Domain

Theorem

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

Proof

Recall that Real Numbers form Field.

The result then follows directly from Field is Integral Domain.

$\blacksquare$

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 3$. Definition of an Integral Domain