## What is an Infinite Discontinuity?

An **infinite discontinuity** has one or more infinite limits—values that get larger and larger as you move closer to the gap in the function. An infinite discontinuity is a subtype of essential discontinuities, which are a broad set of badly behaved discontinuities that cannot be removed.

It’s important to note that only

**one side**has to tend to ±infinity in order for the discontinuity to be classified as infinite. One side may reach a certain function value, or be undefined. But as long as one side is either negative infinity or positive infinity, then it’s an infinite discontinuity.

## Infinity can be Positive or Negative

The function can go towards infinity in the same direction, or in different directions. For example, the function can go towards:

- Positive infinity on both sides,
- Negative infinity on both sides, or
- One side can go to negative infinity and the other towards positive infinity.

## References

Infinite Discontinuity. Retrieved October 29, 2019 from: http://www-math.mit.edu/~djk/18_01/chapter02/example03.html

Infinite Discontinuities. Retrieved October 28, 2019 from: https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-5-discontinuity/MIT18_01SCF10_Ses5c.pdf

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**Stephanie Glen**. "Infinite Discontinuity: Definition, Examples" From

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