o: Yes, Socrates, but I don't see how he will do it.

Socrates: Neither does he. But I do. Watch! (turning to
the boy) Now I am going to tell you something you don't know,
so Meno will listen very closely to make sure he agrees that I can
tell you. You know multiplication, boy?

Boy: I thought I had demonstrated that, Socrates?

Socrates: So you have, my boy, has he not Meno?

Meno: Yes, Socrates, I recall he did the other day.

Socrates: And you know the way to undo multiplication?

Boy: It is called division, but I do not know it as well as
multiplication, since we have not studied it as long.

Socrates: Well, I will not ask you to do much division, but
rather I will ask you only whether certain answers may be
called odd or even, and the like. Does that suit you?

Boy: It suits me well, Socrates.

Socrates: Then you know what odd and even are, boy?

Boy: Yes, shall I tell you?

Socrates: Please do. I would love to hear what they teach.

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