Domain of Integer Square Function

From ProofWiki
Jump to navigation Jump to search

Theorem

The domain of the integer square function is the entire set of integers $\Z$.


Proof

The operation of integer multiplication is defined on all integers.

Thus:

$\forall x \in \Z: \exists y \in \Z: x^2 = y$

Hence the result by definition of domain.

$\blacksquare$