Question

Prove that set of rational numbers (q) is countable

Answer 1



An easy proof that rational numbersare countable. A set is countable if you can count its elements. Of course if the set is finite, you can easily count its elements. If the set is infinite, beingcountable means that you are able to put the elements of the set in order just like natural numbers are in order.

Answer 2

The rational numbers Q are countable because the function g : Z × N → Q given by g(m, n) = m/(n + 1) is a surjection from the countable set Z × N to the rationals Q.