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ID: INPUT{id.yaml}

Title: >
  Rational numbers

Definition: >
  The field of rational numbers $\mathbb{Q}$ is the field of fractions of
  the HREF{Integers}[integers] $\mathbb{Z}$.

Parameters:
  a:
    type: Q
  
Comments: 
  comment-field: >
    The rational numbers form a field with respect to the usual
    addition and multiplication.

Formulas: 
  
Programs: 
  program-sage:
    language: Sage
    code: |
      numbers = QQ

References:

Links:
  Wiki:
    title: "Wikipedia: Rational number"
    url: https://en.wikipedia.org/wiki/Rational_number

Similar tables:
  
Keywords:
 
Tags:
- ring
- field
- Abelian group  
- rational

Data properties:
  type: Q
  complete: no

Display properties:
  number-header: >
    $a$

Numbers:
  -5: -5
  -4: -4
  -3: -3
  -2: -2
  -1: -1
  0: 
    number: 0
    equals: HREF{Zero}
  1: 
    number: 1
    equals: HREF{One}
  2: 2
  3: 3
  4: 4
  5: 5
  -5/2: -5/2
  -3/2: -3/2
  -1/2: -1/2
  1/2: 1/2
  3/2: 3/2
  5/2: 5/2
  -5/3: -5/3
  -4/3: -4/3
  -2/3: -2/3
  -1/3: -1/3
  1/3: 1/3
  2/3: 2/3
  4/3: 4/3
  5/3: 5/3
  -5/4: -5/4
  -3/4: -3/4
  -1/4: -1/4
  1/4: 1/4
  3/4: 3/4
  5/4: 5/4
  -4/5: -4/5
  -3/5: -3/5
  -2/5: -2/5
  -1/5: -1/5
  1/5: 1/5
  2/5: 2/5
  3/5: 3/5
  4/5: 4/5

— preview —

Rational numbers

edit on github

Numbers

$a$

-5:

-5

-4:

-4

-3:

-3

-2:

-2

-1:

-1

-5/2:

-5/2

-3/2:

-3/2

-1/2:

-1/2

1/2:

1/2

3/2:

3/2

5/2:

5/2

-5/3:

-5/3

-4/3:

-4/3

-2/3:

-2/3

-1/3:

-1/3

1/3:

1/3

2/3:

2/3

4/3:

4/3

5/3:

5/3

-5/4:

-5/4

-3/4:

-3/4

-1/4:

-1/4

1/4:

1/4

3/4:

3/4

5/4:

5/4

-4/5:

-4/5

-3/5:

-3/5

-2/5:

-2/5

-1/5:

-1/5

1/5:

1/5

2/5:

2/5

3/5:

3/5

4/5:

4/5

Definition

The field of rational numbers $\mathbb{Q}$ is the field of fractions of the integers $\mathbb{Z}$.

Parameters

$a$

— rational number

Comments

(1)

The rational numbers form a field with respect to the usual addition and multiplication.

Programs

(P1)

Sage

numbers = QQ

Links

[1]

Wikipedia: Rational number

Data properties

Entries are of type: rational number

Table is complete: no