# Really easy proof just don't know where to start

• Oct 26th 2006, 07:35 AM
action259
Really easy proof just don't know where to start
I got a really easy proof that i know are true but i'm really bad about proving things just need a little help getting started

suppose f:A->B and g:B->C show that g0f is a constant function if either f or g is constant

it is really easy to see that this is true by def but not sure how to formally prove this
• Oct 26th 2006, 07:49 AM
ThePerfectHacker
Quote:

Originally Posted by action259
I got a really easy proof that i know are true but i'm really bad about proving things just need a little help getting started

suppose f:A->B and g:B->C show that g0f is a constant function if either f or g is constant

it is really easy to see that this is true by def but not sure how to formally prove this

We are mapping two non-empty sets by,
$f:A\to B$ such that,
$f(x)=b\in B \, \forall x\in A$
Let,
$g:B\to C$ be any function between two non-empty sets B and C,
Then,
$g \circ f:A\to C$
Is a map between these two sets.
It is,
$g(f(x))=g(b)\forall x\in A$
Thus, it is konstant.

Similary argument in the other direction.