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- Apr 14, 2013

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- Show that the set of all positive rational numbers is a countable set.

(Hint: Consider all points in the first quadrant of the plane of which the coordinates x and y are integers.) - Show that the union of a countable number of countable sets is a countable set.

I have done the following:

- Let $x,y>0$. We write a positive rational $\frac{x}{y}$ at the point (x, y) in the plane in the first quadrant. Now we have to count these points, or not?
- Do we have to use induction here?