## 6.3. Discontinuous Functions

### Examples 6.3.2:

Which of the following functions, without proof, has a 'fake' discontinuity,
a 'regular' discontinuity, or a 'difficult' discontinuity ?

*x = 3*, since we could easily move the single point at

*x = 3*to the right height, thereby filling in the discontinuity.

*x = 0*. We can not change the function at a single point to make it continuous.

*x*gets closer to zero. Assuming that the function does turn out to be discontinuous at

*x = 0*, it definitely seems to have a 'difficult' discontinuity at x = 0.

*x*, the function jumps between 1 and 0 in every neighborhood of

*x*. That seems to mean that the function has a difficult discontinuity at every point.