Question

How do you find an upper bound of a set?

Answer 1

In this question we have to know how to find the upper bound of the set, for this we should know the definition of upper bound which is given by, Any number that is greater than or equal to all of the elements of the set is called an upper bound of a set, so, the upper bound is the smallest of all upper bounds of a set of numbers, and upper bound of a set to be equal to an element.

Complete step-by-step solution:
A function $f$ is bounded in a subset $U$ of its domain if there exist constants M, $m \in \mathbb{R}$ such that
$m \leqslant f\left( x \right) \leqslant M$, for all $x \in U$,
Some sets of numbers have "bounds". That just means that the entire set is on one side of that number .If every number in the set is less than or equal to the bound, the bound is an upper bound. If every number in the set is greater than or equal to the bound, the bound is a lower bound.
If a set of numbers has an upper bound, we say it is bounded from above; if a set of numbers has a lower bound, we say it is bounded from below.
For example: The upper bound of the set \left\\{ {3,2,9,7,4} \right\\} will be equal to 9.

Note: Related concepts are the maximum and the minimum of a set, which are just the largest and smallest elements, respectively. Note that the maximum of a set is always also an upper bound of the set, and the minimum of a set is always also a lower bound of the set.
Every number is an upper bound of the empty set, as well as a lower bound. This is because "every number in the empty set" vacuously satisfies any inequality we'd care to name, since there aren't any.