# Math Help - Well-defined function

1. ## Well-defined function

I need to show that the following formula yields a well-defined function:

f: Z8 --> Z8 defined by f([x]8) = [mx]8 for any m belonging to Z.

2. Originally Posted by page929
I need to show that the following formula yields a well-defined function:

f: Z8 --> Z8 defined by f([x]8) = [mx]8 for any m belonging to Z.
$[x]_8=[y]_8\Longrightarrow [x-y]_8=[0]_8\Longrightarrow [m(x-y)]_8=[mx-my]_8=[0]_8\Longrightarrow [mx]_8=[my]_8$

Tonio