# What does it mean when it says: "non-removable discontinuity at x=4"?

##### 1 Answer

See the explanation.

#### Explanation:

Here is the definition I am familiar with.

Function **discontinuity** at

(This allows us to avoid saying, for example that

**removable discontinuity** at

**non-removable discontinuity** at

**In the most familiar functions:**

Rational and trigonometric functions have non-removable discontinuities at their vertical asymptotes. (Holes are removable.)

Piecewise-defined functions can have jump discontinuities, which are non-removable. (Holes are removable.)

The Greatest integer function (a.k.a. the Floor function) has a non-removable discontinuity at every integer.