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# Sequences watch

1. (Original post by Rose86)
[...]
What have you tried? For the first part: can you see why ? (hint: )
2. (Original post by Zacken)
What have you tried? For the first part: can you see why ? (hint: )
Yes, but I dont know how to define C=...
3. (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?
4. (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+...
5. (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 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?
6. (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 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
7. (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 so how large can become? How large can become?

It may help if you think of a specific set A with a positive infimum e.g.
8. (Original post by Zacken)
What is your definition of supremem?
I guess it's the same as the definition of supremum?
9. (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 to show this.
10. (Original post by atsruser)
If L = inf A > 0, then by definition, for all so how large can become? How large can become?

It may help if you think of a specific set A with a positive infimum e.g.
I know that when I put bigger and bigger number then it will be arbitary close to zero, nacer will be zero
11. (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...
12. (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...
13. (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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