Im reading "discrete mathematics with application" by Sussanne epp and there is a definition of functions based on sets, it is as follow:
"A function F from a set A to a set B is a relation with domain A and a co-domain B that satisfies the following two properties:
1. For Every element x in A, there is an element y in B such that (x,y) E F [ (x,y) belongs to F] .
2. For all elements x in A and y and z in B, if (x,y) E F and (x,z) E F, then y=z."
I understand the first property but i have a doubt regarding the second. What if the function F(x) =√x?
In that case doesn't F(x) have two values for positive real numbers? And so if x = 4 by property 2 we would have -2 = 2.
What am i missing? What am i not understanding?
Are functions different for sets?