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, and let there be is a mapping . If , so is also in . And so is a composition of .
My question is, what exactly is ? Is it the set x ? And are and therefore and ? Because, in the set definition , you have a mapping from ?
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.
I *think* that this example was a prelude to an introduction to matrixes. (Doh)