Just out of curiosity
if I have the function F and G. So that G is the left inverse of F. Because G o F = Idx.
My question is why is it named "left" inverse if it is like that? Is it because of the position of G in the composition notation in relation to F (G is at the left of F in the G o F = Idx equation)?
Another possible guess would be :
it's called a "left " inverse of F because to do G o F = Idx means that it goes from the domain to the codomain, then back to the domain again (the domain is usually illustrated at the left)
It's called a "right" inverse F because to do F o H = Idy means that it goes from the codomain to the domain, then back to the codomain again (the codomain is usually illustrated at the right side).
Or is it named "left/right" inverse because of some other reason? Does anybody knows the answer?