Expert: Ahmed Salami - 9/30/2004

Question
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Followup To
Question -
Must not a compact set be infinite?
Answer -
Hi jsquarek,
A set S of real numbers is compact if and only if it is closed and bounded. A set then doesn't have to be infinite for it to be closed or bounded e.g [0,10]for only integers.
Regards.

Upon further thought, I seem to have some issues with your answer:

1.  The integers are not bounded in the sense used in your definition of "compact".  Which is to say, all the defintitions of "bounded" which I find in my books which would apply here, involve infinite sequences of set members.

2.  If your example of [0,10] of integers is not compact, are we then back to compact sets of necessity having an infinite number of members?  

Answer
Hi jsquarek,
I'm sorry that i'm just attending to you. Like i said before, i'm not able to really rigorously give explanations on topics relating to real analysis and topology at the moment.
Just to add, i infact meant that [0,10]was compact. I'm sorry i'm not able to say more at this time.
Regards.