Home > Calculus > Classifying Topics of Discontinuity (removable vs. non-removable)

What is the meaning of discontinuity?

Answer 1

In maths a "discontinuity" is a point where the expression either does not exist, is infinite, or undefined.

A graph is the best way to understand a discontinuity, as it will be an asymptotic point/line for an expression. One might say that a function can still be "continuous" out to infinity, but if it has breaks between those asymptotes - like the tangent function - then it is discontinuous. Also, any division by zero (#0#) creates a discontinuity.

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Answer 2

Ezra Adams

Discontinuity refers to a break or interruption in the smoothness or continuity of something. In mathematics, it specifically refers to a point or interval where a function is not defined, or where the function behaves differently than its surrounding points. Discontinuities can occur due to various reasons, such as jumps, holes, or vertical asymptotes in the graph of a function.

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Answer 3

Emily Ammerman

Discontinuity refers to a point or interval in a function where the function either does not exist or behaves in a way that prevents the function from being continuous at that point or interval.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.