# Determine if it is countable or uncountable

Determine if it is countable or uncountable The set $E$ of all circle in $R$$^2 with centers at rational coordinate points and positive rational radius. I have no idea about this type of question. - ## 2 Answers Hints: 1) If sets A and B are countable then their cartesian product A\times B is countable. 2) Note that every element of E is represented by a triple (x,y,r) with x,y\in \mathbb Q and r\in \mathbb Q^{+} - Hint: if you can find a surjective mapping from a countable set to the set E you are looking at, you will prove the set E is countable. Try finding a surjection from \mathbb Q\times\mathbb Q\times\mathbb Q_+ to E. - Don't you need \mathbb Q\times\mathbb Q\times\mathbb Q to E? As you have a rational radius as well. – Cruncher Feb 24 '14 at 15:53 Correct. Even more correct, it's \mathbb Q\times \mathbb Q\times \mathbb Q_+ – 5xum Feb 24 '14 at 19:15 Still not 100% understand... How about the R$$^2$?? Is it mean real number? So it is uncountable?? – user109403 Feb 25 '14 at 2:04
No, because you can't have a circle with the center at $(\sqrt 2, 5)$. – 5xum Feb 25 '14 at 6:26