This shall not study this general case, but it note two especially useful ways
of generalizing Definition 4.21. Suppose first that the domain A of f contains
the open interval (a, d) for some d > a.

Definition 4.23 : The right-hand limit lim f(x) [x→a+] is equal to l if given ε > 0
there exists δ > 0 such that |f(x) − l| < ε for all x in (a, a + δ). Note that δ may be
chosen small enough so that (a, a + δ) ⊆ (a, d), and therefore f(x) is defined
for all x in (a, a + δ). Left-hand limits are defined similarly.