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

[Crutcher Dunnavant]

Doing some reading this week, I decided to probe those two definitions we
were hitting in this last chapter: injective and surjective

Having never made it to abstract algebra, I'd not seen them before. William
Lawvere introduces them without a good discussion.

So I discovered that the wikipedia articles on the subject are quite good:

http://en.wikipedia.org/wiki/One-to-one - this is Injection
http://en.wikipedia.org/wiki/Surjection
http://en.wikipedia.org/wiki/Bijective_function

The fun thing is: a function f is bijective iff it is both and injective and
surjective.

Make sure to also look at the notion of left and right inverses (retractions
and sections):
http://en.wikipedia.org/wiki/Inverse_function#Left_and_right_inverses

-- 
Crutcher Dunnavant <crutcher at gmail.com>
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