# Continuity proof

• Feb 15th 2009, 11:26 AM
WWTL@WHL
Continuity proof
Question

Show that every function $f: \mathbb{Z} \to \mathbb{R}$ is continuous.

Any ideas?

Thanks.
• Feb 15th 2009, 01:17 PM
ThePerfectHacker
Quote:

Originally Posted by WWTL@WHL
Question

Show that every function $f: \mathbb{Z} \to \mathbb{R}$ is continuous.

Any ideas?

Thanks.

For every $\epsilon > 0$ let $\delta = \tfrac{1}{2}$ then the $\delta$-neighorhood of $n\in \mathbb{Z}$ contains only itself in $\mathbb{Z}$.
• Feb 15th 2009, 01:25 PM
WWTL@WHL
And done.

Excellent. Thank you, PH.