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A discontinuity is a point in a function where the function is either undefined, or is disjoint from its limit.

## Jump discontinuity

A jump discontinuity occurs when right-hand and left-hand limits exist, but are unequal. That is:

$\lim_{x\to a^+}f(x) \ne \lim_{x\to a^-}f(x)$

## Removable discontinuity

A removable discontinuity occurs when left-hand and right-hand limits exist and are equal, but are undefined for the specified value.

Example: $\lim_{x\to 0}\frac{sin x}{x} = 1$

## Infinite discontinuity

An infinite discontinuity occurs at points wehre the left-hand and right-hand limits are infinite.

Example: $\lim_{x\to 0^+}\frac{1}{x} = \infty$ and $\lim_{x\to 0^-}\frac{1}{x} = -\infty$

## Other discontinuities

Other discontinuities exist, such as a value oscillating as it approaches a given value.

$\lim_{x\to 0}\sin\frac{1}{x}$
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