Boy: (the boy recites) A number can only be odd or even if it is a whole number, that is has no parts but only wholes of what it measures. Even numbers are special in that they have only whole twos in them, with no ones left over, while odd numbers always have a one left over when all the twos are taken out. Socrates: An interesting, and somewhat effective definition. Do you agree, Meno. Meno: Yes, Socrates. Please continue. Socrates: Now boy, what do you get when you divide these odd and even numbers by other odd and even numbers. Boy: Sometimes you get whole numbers, especially when you divide an even number by an even number, but odd numbers sometimes give whole numbers, both odd and even, and sometimes they give numbers which are not whole numbers, but have parts. Socrates: Very good, and have your teachers ever called these numbers ratios? Boy: Sometimes, Socrates, but usually only with simple numbers which make one-half, one-third, two-thirds and the like. Socrates: Yes, that is usually what people mean by ratios. The learned people call numbers made from the ratios, rational. Does the name rational number suit you to call a number which can be expressed as the ratio of two whole numbers, whether they be odd or even whole numbers? Boy: You want me to call the numbers made from ratios of whole numbers something called rational? A ratio makes a rational number? Socrates: Yes boy, can you do that? Boy: Certainly, Socrates. Socrates: Do you agree with the way I told him this, Meno? Does it violate our agreement? Meno: You added -nal to the word ratio, just as we add -nal to the French word "jour" to create the word journal which means something that contains words of the "jour" or of today. So we now have a word which means a number made from a ratio. This is more than acceptable to me, Socrates. A sort of lesson in linguistics, perhaps, but certainly not in mathematics. No, I do not see that you have told him how to solve anything about the square root of two, but thank you for asking. I give you your journalistic license to do so. Socrates: Good. Now boy, I need your attention. Please get up and stretch, if it will help you stay and think for awhile. Boy: (stretches only a little) I am fine, Socrates. Socrates: Now think carefully, boy, what kind of ratios can we make from even numbers and odd numbers? Boy: We could make even numbers divided by odd numbers, and odd numbers divided by even numbers. Socrates: Yes, we could. Could we make any other kind? Boy: Well... we could make even numbers divided by even numbers, or odd numbers divided by odd. Socrates: Very good. Any other kind? Boy: I'm not sure, I can't think of any, but I might have to think a while to be sure. Socrates: (to Meno) Are you still satisfied. Meno: Yes, Socrates. He knows even and odd numbers, and ratios; as do all the school children his age.