Determine if function is well defined I am having difficulties determining if the following function is well defined:
On certain computers the integer data type goes from $-2, 147, 483, 648$ through $2, 147, 483, 647$. Let S be the set of all integers from $-2, 147, 483, 648$ through $2, 147, 483, 647$. Try to define a function $f:S  -> S$ by the rule $f(n) = n^2$ for each n in S. Is f well defined? Why?
Side notes:
I am learning how to determined whether a function is well defined. I am doing so by relying on two disticnt reasons that show a not well defined function: (1) There is no y that satisfies  the given equation or (2) there are two different values of y that satisfy the equation. 

$n = 2, 147, 483, 647 \in S$.
Is there any $f(n) = y \in S$ such that $$y = (2, 147, 483, 647)^2\quad?$$
Indeed, for any integer $n \gt 46340, n^2 \notin S$.
How does this relate to the first reason you give for a function not being well-defined?
