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# Upper Bound Definition

The upper bound of a function C exists for a function f if the condition f(x) ≤ C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it has an upper bound. In other terms the upper bound is any number that is greater than or equal to all of the elements of the set. For instance, 6 is an upper bound of the interval [0,1]. As are the numbers 5, 4, 3, 2, and 1.

### Sources

“Upper Bound.” From Wolfram MathWorld, mathworld.wolfram.com/UpperBound.html.

“Upper Bound of a Set.” Mathwords, www.mathwords.com/u/upper_bound.htm.

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