# What is a removable discontinuity?

##### 1 Answer

Please see the explanation section, below.

#### Explanation:

Recall that:

a function, **if and only if**

Furthermore,

**if and only if**

(i)

#lim_(xrarra)f(x)# exists,(ii)

#f(a)# exists , and(iii) the numbers in (i) and (ii) are equal.

**if and only if**

This mean that

**Discontinuities in general**

Many presentations of calculus do not give a precise definition of "

Mathematicians generally mean something like: **and**

(At other times, mathematicians seems to mean *continuous* near **and**

For example, The square root function (as a function