CMSC 250 Lecture Notes - Lecture 8: Surjective Function, Injective Function
6 Jul 2017
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There can be more than 1, but at least 1 has to map to it. A surjective function, or onto function is a function where for every (cid:1877) value, there is a (cid:1876) value. We must tell you the domain or codomain for you to answer: domain and codomain is all real numbers. No, since -1(or any negative) is never mapped to: domain is all real numbers, codomain is real numbers greater than zero. Yes, this is surjective: domain is natural numbers, codomain is squares. An injective function or one to one function is when every element of the codomain is mapped to at most one element of the domain. We didn"t say every element in the codomain had to be mapped to. We just said if they were mapped to, they would need to have at most 1 mapping to be valid. Ex: is (cid:1876)2 injective: domain is all real numbers, codomain is all real numbers.
