Give an example of a bounded non-empty set of real numbers which hasa supremum, but does not have a maximum. Justify your answercarefully.

Question

Give an example of a bounded non-empty set of real numbers which hasa supremum, but does not have a maximum. Justify your answercarefully.
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

An example of a bounded non-empty set of real numbers which has a supremum but does not have a maximum is the open interval (0,1) on the real number line.

Step 1: Define the set Let's define the set S = {x ∈ R : 0 < x < 1}. This is the set of all real numbers between 0 and 1, not including 0 and 1 Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

Give an example of a bounded non-empty set of real numbers which hasa supremum, but does not have a maximum. Justify your answercarefully.

Let A and B be non-empty bounded subsets of R. DefineA − B := {a − b : a ∈ A, b ∈ B}.Prove thatsup(A − B) = sup A − inf B

Let A and B be non-empty bounded subsets of R. DefineA − B := {a − b : a ∈ A, b ∈ B} .Prove thatinf(A − B) = inf A − sup B

1. {x: x is an integer neither positive nor negative} is ________a) Empty setb) Non-empty setc) Finite setd) Non- empty and Finite set

The graph given below is an example of _________     A. semilatticeB. non-lattice posetC. partial latticeD. bounded lattice

1/3