[formal-methods] Injective, Surjective, and Bijective functions

[d p chang]

Mikael Vejdemo-Johansson <mik at stanford.edu> writes:

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> On Jun 26, 2009, at 4:55 PM, Crutcher Dunnavant wrote:
>
>> On Fri, Jun 26, 2009 at 7:20 AM, d p chang <pchang at macrovision.com>  
>> wrote:
>> Jason Dusek <jason.dusek at gmail.com> writes:
>>
>> >   The notion of injection and surjection apply specifically to sets
>>
>> this does include 'infinite' sets?
>
> The definitions certainly make sense for infinite sets as well. 

thanks. this was my understanding, but wanted to make sure hadn't missed
some subtlty.

> For instance, the map (*2): Z -> Z is injective (prove it!) but not
> surjective (prove it!), and is an establishing map for why infinities
> are weird.

:-)

surjective seems 'easy' by counterexample. 

i'm not sure i have the 'notation' for reasoning/expressing that the
infinities are equal, but it seems like one of those questions i
associate w/ cantor and diagonals.

\p
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