Surjective Functions

This video introduces onto, or surjective, functions and includes examples and nonexamples. Essential sections are 0:00-4:08 and 5:20-6:39. Section 4:09-5:19 discusses a function defined on a set of matrices, and Section 6:40-7:48 discusses the function from the set of all integers to the set {0,1,2,3,4} defined by sending each integer n to n mod 5 (the remainder obtained when n is divided by 5). In the Concept Check at the end of the video (7:48-9:02), f should be defined as follows: for each rational number r in ℚ, write r in the form r = a/b, where a and b are integers, b is positive, and either a = 0, or a and b have no positive common prime factor except 1. Then define f (r) = f (a/b) = a. (Example 7.1.12 in Section 7.1 shows that if a and b are not specified in this way, f is not well-defined.)

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