Domains, codomains, and morphisms

If we look closely, we can find ordered pairs of data all around us. Let's look at some statistics of Lionel Messi. The following table shows how many goals Messi scored for 10 consecutive years:

We say that the domain is set A:{2007, 2007, 2007, 2010, 2011, 2012, 2013, 2014, 2015, 2016} and the range (or codomain) is set B:{5, 6, 7, 8, 10} and that the ordered pairs are {(2007,10), (2008, 6), (2008, 8), (2010, 5), (2011, 8), (2012, 5), (2013, 5), (2014, 7), (2015, 6), (2016, 10)}.

Each year maps to a number of goals scored.

If the year where x and y was calculated by calling a function named f, we could get y by calling f(x). For example, f(2010) = 5 and f(2016) = 10.

Does the following relation make sense?

How can Messi score exactly 6 goals and exactly 7 goals and exactly 10 goals in the same year? That makes no sense, right? (Right!)

We can say that the relation of {(2007, 6), (2007, 7), (2007, 10)} which is defined by our arrows is not a function because...