How is this a function? - Analysis. 
Let $X = \{1, 2, 3\}, Y = \{4, 5, 6\}$. Define $F \subseteq X \times Y$ as
$F = \{(1, 4),(2, 5),(3, 5)\}$.
Then $F$ is a function.

I simply do not see how this could be a function, as there is nothing that it is mapping to, if anyone can explain how this is a function, that would be lovely.

Recall that a function is comprised of three parts:

*

*Domain

*Codomain

*The way to uniquely associate every element in its domain to an element in its codomain

So it's perfectly OK to denote a function $f$ as the set of all pairs $(x, f(x))$, since it encodes all the necessary information to represent a function.
