What is jump Discontinuity?

1 Answer
Amory W.
Aug 19, 2014

lim_(x->a^-)f(x), lim_(x->a^+)f(x) are finite and lim_(x->a^-)f(x)!=lim_(x->a^+)f(x). So it occurs when the left and right limit at a do not match, then we say f(x) has a jump discontinuity at a.

This should not be confused with a point discontinuity where:

lim_(x->a^-)f(x)=lim_(x->a^+)f(x)

which means

lim_(x->a)f(x) exists

and:

lim_(x->a)f(x)!=f(a)

It could be the case that f(a) is finite or simply DNE.

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