Injective vs. Bijective

functions

What's the difference between Injective and Bijective? For example, is there a more rigorous proof of the bijectivity of a function? Also, can these properties be applied to more than just functions? Thank you!


Imagine you have some number of buckets and some number of balls. Your "mapping" is putting balls into buckets. Then the map is

  • surjective if every bucket has at least one ball;

  • injective if every bucket has at most one ball;

  • bijective if every bucket has exactly one ball.

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