Category:Modulo Addition is Well-Defined

This category contains pages concerning Modulo Addition is Well-Defined:

Let $m \in \Z$ be an integer.

Let $\Z_m$ be the set of integers modulo $m$.

Let $\eqclass a m$ denote the equivalence class on $\Z_m$, for some $a \in \Z$.

The modulo addition operation on $\Z_m$, defined by the rule:

$\eqclass a m +_m \eqclass b m = \eqclass {a + b} m$

is a well-defined operation.

That is:

If $a \equiv b \pmod m$ and $x \equiv y \pmod m$, then $a + x \equiv b + y \pmod m$.