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Topic: Definitions of function type - injection
Replies: 5   Last Post: Sep 26, 2013 5:18 PM

 Messages: [ Previous | Next ]
 Peter Luschny Posts: 26 Registered: 11/18/06
Re: Definitions of function type - injection
Posted: Sep 6, 2013 3:27 AM

> > > 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.

Date Subject Author
9/5/13 Aaron Gray
9/5/13 Axel Vogt
9/5/13 Peter Luschny
9/5/13 Aaron Gray
9/6/13 Peter Luschny
9/26/13 Aaron Gray