Integers form Subring of Reals
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Theorem
The ring of integers $\struct {\Z, +, \times}$ forms a subring of the field of real numbers.
Proof
We have that the set of integers $\Z$ are a subset of the real numbers $\R$.
The field of real numbers is, a fortiori, also a ring.
Hence the result, by definition of subring.
$\blacksquare$
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 56$. Subrings and Subfields
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): subring