> > > Is this a strong enough and correct definition of injection ? > > > X ? Y = ?x?X. ?y?Y ? x ? y > > No. Your expression does not capture the 'at most' in the definition of injective. > Can you give me a better definition ?
Well, to get the 'at most' part in the definition of injective, consider the following: assume a and b (elements of X) are mapped to an y (element of Y).
a -> y b -> y
This scenario is to be excluded in the case that a does not equal b. So you can say:
If such a situation arises then a is forced to be identical to b.