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?
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 One-to one function or Injective function. "[/url]
Forum for the GRE subject test in mathematics.
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