In the book that I'm currently reading it states that:
"Two maps can be applied one after the other provided the co-domain of the first map is the same as the domain of the second. This process is called composition of maps"
I'm just curious as to know whether this statement is fully accurate? Shouldn't it actually be something more around the lines of:
"Two maps can be applied one after the other provided the image set of the first map (say, Im(f) where the map is f) is a subset of the domain of the second"
Both statements are sufficient for the composite function to be well defined.
All we need is that for every $x$ in the domain of $f$, we can define $g(f(x))$ so $f(x)$ should be in the domain of $g$