# Fractional numbersΒΆ

The type of fractional numbers is written F, π½, Frac, or Fractional. The fractional numbers include all the natural numbers (0, 1, 2, β¦) along with all the positive fractions formed from the ratio of two natural numbers (such as 1/2, 13/7, 56/57, β¦)

Adding, multiplying, or dividing two fractional numbers yields another fractional number. Trying to subtract two fractional numbers will automatically convert the result to a rational number:

Disco> :type (1/2) * (2/3)
1 / 2 * 2 / 3 : π½
Disco> :type 1/2 - 2/3
1 / 2 - 2 / 3 : β


The special sets β (natural numbers), β€ (integers), and β (rational numbers) are very common in mathematics and computer science, but the set of fractional numbers π½ is not common at all (in fact, I made up the name and the notation). People usually start with the natural numbers β, extend them with subtraction to get the integers β€, and then extend those again with division to get the rational numbers β. However, there is no reason at all that we canβt do it in the other order: first extend the natural numbers β with division to get the fractional numbers π½, then extend with subtraction to get β. Having all four types in Disco (even though one of them is not very common in mathematical practice) makes many things simpler and more elegant.