Continuity

Definition

Continuity describes whether or not there are any breaks, holes, or jumps in a function. A continuous function has no interruptions and can be drawn without lifting your pen from the paper.

Related terms

Discontinuity:

Discontinuity occurs when there are breaks, holes, or jumps in a function.

Intermediate Value Theorem (IVT):

The IVT states that if you have two points on either side of some value within an interval where a continuous function exists, then there must be at least one point within that interval where the function takes on every value between those two points.

Removable Discontinuity:

A removable discontinuity is when there's initially an interruption in the graph of a function but can be fixed by redefining its value at that particular point.