# composition of relations

• Apr 4th 2009, 01:14 AM
bmp05
composition of relations
Hello, I'm having problems undestanding an example. It's supposed to be simple, but I can't quite draw the conclusions.

Let there be a Set, $M$ and let there be $Map(M, M) := \{f~|~ f: M \rightarrow M$ is a mapping $\}$. If $f, g \in Map(M, M)$, so is $f \circ g$ also in $Map(M, M)$. And so is $\circ$ a composition of $Map(M, M)$.

My question is, what exactly is $Map(M, M)$? Is it the set $M$x $M$? And are $f$ and $g$ therefore $Map(f, f')$ and $Map(g, g')$? Because, in the set definition $Map(M, M) := \{f~|~ f: M \rightarrow M\}$, you have a mapping from $M \rightarrow M$?
• Apr 4th 2009, 01:45 AM
bmp05
Oh! This is about the image of a function?! And M is the domain, and codomain of the two functions f and g?! Still, if that's right, it's hard to understand from the example. So the example is saying that a composition exists for any two functions if they share the same domain and codomain.
• Apr 4th 2009, 09:16 AM
bmp05
I *think* that this example was a prelude to an introduction to matrixes. (Doh)