The way I see it if f: A > B
surjection: EVERY element of B receives a map from A. Multiple elements of A can map to the same B.
injection: EVERY element of A maps to a unique element of B. Can there be B's left unmapped?
bijection (both surjective and injective): EVERY element of A maps to a unique element of B. There are no B's left unmapped, ie. # elements in A = # elements in B
Question1: Can the function that maps the empty set to the empty set be considered any of these?
Question 2
Many definitions of injective functions has been as follows and it leads me to think that in an injective function all elements of B receive a map. Is it true? I think not but I just want to make sure it is clear:
"If we have a function f : A > B, such that every element of B is mapped onto by one and only one element of A the function is called a Oneto one function or Injective function. "[/url]
surjection, injection and bijection clarification

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 Joined: Sun Oct 07, 2007 1:49 pm