Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    Name:  IMG_7497.jpg
Views: 18
Size:  500.4 KB
    Offline

    22
    ReputationRep:
    (Original post by Rose86)
    [...]
    What have you tried? For the first part: can you see why a\neq 0? (hint: \inf(A) > 0)
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    What have you tried? For the first part: can you see why a\neq 0? (hint: \inf(A) > 0)
    Yes, but I dont know how to define C=...
    Offline

    22
    ReputationRep:
    (Original post by Rose86)
    Yes, but I dont know how to define C=...
    You don't need to define C, the definition has been given to you?
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    You don't need to define C, the definition has been given to you?
    I mean I dont know how to use this equation C=1/a+...
    Offline

    22
    ReputationRep:
    (Original post by Rose86)
    I mean I dont know how to use this equation C=1/a+...
    First off, it's not an equation. Second off, to ensure that the object (1/a) + b exists, that is, C is well-defined, you need to ensure that a \neq 0 where a is a general element of A. Can you see why this is true?

    Second, you need to show that the supremem of C exists. What is your definition of supremem? How can you apply it here?
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    First off, it's not an equation. Second off, to ensure that the object (1/a) + b exists, that is, C is well-defined, you need to ensure that a \neq 0 where a is a general element of A. Can you see why this is true?

    Second, you need to show that the supremem of C exists. What is your definition of supremem? How can you apply it here?
    Sorry, i used word equation because English is not my first Language
    Offline

    11
    ReputationRep:
    (Original post by Rose86)
    I mean I dont know how to use this equation C=1/a+...
    If L = inf A > 0, then by definition, for all a \in A, a \ge L so how large can 1/a become? How large can \frac{1}{a}+b become?

    It may help if you think of a specific set A with a positive infimum e.g. A=(\frac{1}{10}, \infty)
    Offline

    11
    ReputationRep:
    (Original post by Zacken)
    What is your definition of supremem?
    I guess it's the same as the definition of supremum?
    Offline

    11
    ReputationRep:
    (Original post by Rose86)
    Sorry, i used word equation because English is not my first Language
    We really ought to use a different symbol here, to indicate a definition, rather than equality. Often people write C := \{ \cdots \} to show this.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by atsruser)
    If L = inf A > 0, then by definition, for all a \in A, a \ge L so how large can 1/a become? How large can \frac{1}{a}+b become?

    It may help if you think of a specific set A with a positive infimum e.g. A=(\frac{1}{10}, \infty)
    I know that when I put bigger and bigger number then it will be arbitary close to zero, nacer will be zero
    Offline

    17
    ReputationRep:
    (Original post by Rose86)
    I know that when I put bigger and bigger number then it will be arbitary close to zero, nacer will be zero
    The question was how large 1/a can become, not how small...
    Offline

    22
    ReputationRep:
    (Original post by Rose86)
    I know that when I put bigger and bigger number then it will be arbitary close to zero, nacer will be zero
    To complement what the others are saying, in a purely unrigorous, informal way - the intuition here should be: you want to make (1/a + b) as big as possible. Which means making b as big as possible and (1/a) as big as possible. To make the latter as big as possible, you should make a as small as possible, etc...
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    To complement what the others are saying, in a purely unrigorous, informal way - the intuition here should be: you want to make (1/a + b) as big as possible. Which means making b as big as possible and (1/a) as big as possible. To make the latter as big as possible, you should make a as small as possible, etc...
    Thank you
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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