# Well-defined function

• Oct 4th 2010, 02:58 PM
page929
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.
• Oct 4th 2010, 04:46 PM
tonio
Quote:

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