Turn on thread page Beta
    • Thread Starter

    if X={a : a is in the reals} is supX=a?

    No it wouldn't be. The set you have given is the set of real numbers. So saying Sup(X)=a doesn't make any sense as a just used to denote an element of the set not a specific number. It is the set of all numbers a such that a is a real number.

    Note that Sup(X) doesn't necessarily exist.

    Think about the set you are talking about, suppose that the set you have given has a supremum then that number we will call N has the property that N is greater than or equal to all elements of the set you have given and it is the smallest such number to have this property.

    Now can you think of a number that is greater than or equal to every real number?

    Hopefully you should see that the answer to the previous question would be no simply by the fact there are infinitely many real numbers.

    Hence sup(X) can't exist.

    (Original post by asdfyolo)
    if X={a : a is in the reals} is supX=a?
    I guess you meant something like X=\{x \in \mathbb{R} : x=a\} ? What you have written is at best ambiguous.
Submit reply
Turn on thread page Beta
Updated: October 30, 2015


students online now


Exam discussions

Find your exam discussion here

Should predicted grades be removed from the uni application process
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.