ABSTRACT
When we say that a function f : D → R has a limit at the point c, it is tacitly assumed that c is a cluster point of D, which may or may not belong to D. In general, limx→c f(x) has no relation to f(c), the value of f at c. For example the function defined on R by
f(x) = ½
x2, x 6= 2 5, x = 2
has a limit at every point c ∈ R, including the point 2, given by c2. This coincides with the value of f at c, except when x = 2. At x = 2 we have f(2) = 5 6= limx→2 f(x) = 22 = 4.
