Define a function as follows:

- If ;
- .

- The discontinuity at 0 of is not removable, as has two infinite one-sided limits at 0 (see Figure 2(d)).
- The discontinuity at 1 of is removable, as has a finite limit, equal to 2, at 1 (see Figure 2(e)).
- Let , defined over . We can easily prove that has a limit at 0 and that this limit is equal to 1. Thus 0 is a removable discontinuity of .

This means that has a removable discontinuity at 0.

Noah Dana-Picard 2007-12-28