# Proof of union

1. Oct 13, 2008

### fk378

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. Oct 13, 2008

### CompuChip

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"?

3. Oct 13, 2008

### fk378

I mean that the union of all those intervals from 1 to infinity IS N.

4. Oct 13, 2008

### CompuChip

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