Q. 23 - Calculus

Question

Make a statement expressing a property analogous to the least upper bound property for nonempty subsets of real numbers that are bounded below.

Step-by-Step Solution

Answer

Consider S is a nonempty subset of real numbers and m is a real number such that the element of the subset $x\in S \& x\ge m$then m is said to be the greatest lower bound. 

Step 1. Given information.

The given topic that needs to be explained is the least upper bound property for nonempty subsets of real numbers.

Step 2. Explanation.

The property that is analogous to the least upper bound property for nonempty subsets of real numbers that are bounded below is The greatest lower bound property.

The greatest lower bound property for nonempty subsets of real numbers. 

Consider S is a nonempty subset of real numbers and m is a real number such that the element of the subset $x\in S \& x\ge m$then m is said to be the greatest lower bound. 

The greatest one among all lower bounds is known as the greatest lower bound.