Rose86
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Zacken
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(Original post by Rose86)
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What have you tried? For the first part: can you see why a\neq 0? (hint: \inf(A) > 0)
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Rose86
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(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=...
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Zacken
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(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?
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Rose86
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(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+...
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Zacken
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(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?
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Rose86
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(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
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atsruser
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(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)
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atsruser
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(Original post by Zacken)
What is your definition of supremem?
I guess it's the same as the definition of supremum?
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atsruser
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(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.
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Rose86
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(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
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DFranklin
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(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...
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Zacken
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(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...
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Rose86
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(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
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