Does the Limit Exist at a Jump Discontinuity?

Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.

Do jump discontinuities have limits?

Removable discontinuities can be "fixed" by re-defining the function. The other types of discontinuities are characterized by the fact that the limit does not exist. Specifically, Jump Discontinuities: both one-sided limits exist, but have different values.

Is there a limit at an infinite discontinuity?

In an infinite discontinuity, the left- and right-hand limits are infinite; they may be both positive, both negative, or one positive and one negative.