Socrates: Yes, my boy, er, ah, sir.
Boy: We want to see if this square root of two we discovered the other day is a member of the rational numbers?
Socrates: Yes.
Boy: So we define the rational numbers as numbers made from the division into ratios of whole numbers, whether those whole numbers are even or odd.
Socrates: Yes.
Boy: We get four groups, even over even, which we don't use, odd over even, odd over odd, and even over odd.
Socrates: Continue.
Boy: We know the first number in the squared ratio cannot be odd because it must be twice the value of the second number, and therefore is must be an even number, two times a whole number. Therefore it cannot be a member of either of the next groups, because they both have whole numbers over odd numbers.
Socrates: Wonderful!
Boy: So we are left with one group, the evens over odds.