Mappings and Inverses: More Than One Left Inverse?

[kidsmoker]

Hi,
just re-reading my lecture notes and there's a bit where it says

"The same mapping may have more than one left inverse (if it is not surjective) and more than one right inverse (if it is not injective)."

I can see how a mapping could have more than one right inverse. But how could it have more than one left inverse? This implies that you have one element from the domain being mapped to two different elements in the codomain. But my definition of a map is

"If A and B are sets then a mapping from A to B is a rule which associates to each element of A one and only one element of B".

Surely this is a contradiction?

Thanks for your help.

 

[Vid]

The different left inverses are for different values of the elements in the codomain that don't have inverse because f is not onto.

 

[kidsmoker]

Ah i see. Thanks!