On Friday, 6 September 2013 08:27:29 UTC+1, peter....@gmail.com wrote: > > > > 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. > > > > This statement now is easy to formalize.
Okay, found better definitions now and realized I was actually interested in in both total and partial surjection.