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injective or surjective whats the difference?

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(a) What does it mean for a function to be injective (1-1)? (b) What does it mean for a function to be surjective (onto)? (c) Give an example of a function on the integers that is 1-1 but not onto. (d) Give an example of a function on the integers that is onto but not 1-1.

Apr 21st, 2015

a) an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

b) The function f : R → R defined by f(x) = 2x + 1 is injective.

c) A surjective function is a function whose image is equal to its codomain. Equivalently, a function f with domain X and codomain Y is surjective if for every y in Y there exists at least one x in X with

d) The function f : RR defined by f(x) = 2x + 1 is surjective (and even bijective), because for every real number y we have an x such that f(x) = y: an appropriate x is (y − 1)/2.

Apr 21st, 2015

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