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Re: a collection of sets
Posted:
Jan 2, 2009 12:27 AM


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.



