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Topic: a collection of sets
Replies: 4   Last Post: Jan 2, 2009 2:36 AM

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Nat Silver

Posts: 2,082
Registered: 12/6/04
Re: a collection of sets
Posted: Jan 2, 2009 12:27 AM
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conrad wrote:
>I have the collection
> E = { { x in R | x^2 < n } | n in N }
> I guess I am having difficulty interpreting
> what the above collection means

For each natural number n, there is a subset of
real numbers x that satisfies the property x^2 < n.

For example, if n = 10, say, then
we have x^2 < 10. This inequality may
be rewritten -srt(10) < x < sqrt(10).

If you are still confused, try n = 9.
Then x^2 < 9, which can be rewritten
-3 < x < 3.

The collection of all (infinitely many) of these
nested sets (open intervals, centered at the origin)
is E.

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