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Proof of union

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that the union of intervals [1,n] from n=1 to n=infinity is all of N.

    3. The attempt at a solution

    Do I use induction on this? Archimedes? (This question is before the section of Archimedes though). I need help on how to start it!
     
  2. jcsd
  3. Oct 13, 2008 #2

    CompuChip

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    Counterexample:
    3/2 is in the union, because it is in [1, n] for, for example, n = 2. But 3/2 is not a natural number.

    Did you mean: "prove that the union contains N"?
     
  4. Oct 13, 2008 #3
    I mean that the union of all those intervals from 1 to infinity IS N.
     
  5. Oct 13, 2008 #4

    CompuChip

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    Since that seems to be false, let's go back a step.
    Do you also use the definitions
    [tex][1, n] = \{ x \in \mathbb R \mid 1 \le x \le n \} [/tex]
    (for [itex]n \ge 1[/itex]) and
    [tex]N = \{ 1, 2, 3, 4, \ldots \}[/tex]?
     
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