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

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Aaron Gray

Posts: 4
Registered: 9/5/13
Re: Definitions of function type - injection
Posted: Sep 26, 2013 5:18 PM
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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.

Many thanks,

Aaron



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