Take a function
defined on a pointed neighborhood
. Suppose that
has a finite limit
Then we say that
has a removable discontinuity
Define a function as follows:
is continuous at
Removable (or not) discontinuity.
Look for a limit of
is the product of a bounded function (as the sine function is bounded over
, we have
) and a function whose limit at 0 is equal to 0.
Therefore, by Theorem thm sandwich, we have
This means that
has a removable discontinuity at 0.
A removable discontinuity.