Open Interval
Definition
An open interval is a set of real numbers between two endpoints, where the endpoints are not included in the interval.
Analogy
Imagine you're at a party and there's a dance floor. The open interval is like the space on the dance floor where people can freely move around, but they don't include the edges of the dance floor.
Related terms
Closed Interval: A closed interval includes its endpoints, so it's like having a rope tied across the edges of the dance floor, restricting movement beyond those points.
Half-Open Interval: A half-open interval includes one endpoint but not the other. It's like having one side of the dance floor blocked by a wall, allowing movement only from one direction.
Infinite Interval: An infinite interval extends indefinitely in one or both directions. It's like having an endless dance floor that stretches as far as you can see in either direction.
"Open Interval" appears in:
Subjects (1)
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Practice Questions (5)
What is the definition of continuity over an open interval?
Is m(x) = 1/(x-2) continuous over the open interval (-1, 3)?
Is g(x) = (x^2 - 1)/(x - 1) continuous over the open interval (-∞, 1)?
Is k(x) = ln(x + 3) continuous over the open interval (-3, ∞)?
If a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), which of the following statements is true?
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