# rational number

## Primary tabs

Defines:
rational
Synonym:
$\mathbb{Q}$
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### alternative definition

Back in my day, we called the rational numebers {p/q : p, q are integers}

-apk

### Re: alternative definition

hopefully q was a non-zero integer in your day :)

### Re: alternative definition

It took you five years to prepare that response?

:)

Cam

### (a,b) definition

In general it has been more usefull, more extensible, to define ”rational numbers” as a pair (a,b) with a multiplication and addition rule. And then take Integers as an example.

Addition rule (a,b)+(c,d) (a*d+b*c,b*d)

Multiplication rule: (a,b)*(c,d) (a*c,b*d)

a,b,c,d ∈Z and b,d != 0

Definitions like this allow one to manipulate items from a more general ring and also use the usuall nomeclature a/b=c/d . This includes certain exotic cases in Algebraic Geometry.