My proof:
We know that rational numbers can be written as the form p/q, where p, q are an element of Z, q cannot be 0. This means that we can write all the sets down:

{0/1 0/2 0/3 0/4 0/5 0/6 0/7 ................}
{1/1 1/2 1/3 1/4 1/5 1/6 1/7 ................}
{2/1 2/2 2/3 2/4 2/5 2/6 2/7 ................}
{3/1 3/2 3/3 3/4 3/5 3/6 3/7 ................}
{.....................................…

We can also do the same for negative numbers. As we can see, the numbers are countable because the nth number matches the nth sequence. Hence, we can conclude that the rational
numbers are countable.

How does it sound?

View the original article here