# Category:Rational Numbers

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This category contains results about **Rational Numbers**.

Definitions specific to this category can be found in Definitions/Rational Numbers.

A number in the form $\dfrac p q$, where both $p$ and $q$ are integers ($q$ non-zero), is called a **rational number**.

The set of all **rational numbers** is usually denoted $\Q$.

Thus:

- $\Q = \set {\dfrac p q: p \in \Z, q \in \Z_{\ne 0} }$

## Subcategories

This category has the following 15 subcategories, out of 15 total.

### C

### F

### G

- Gaussian Rationals (2 P)

### I

- Integer Reciprocal Space (13 P)

### R

- Rational Division (2 P)
- Rational Subtraction (1 P)

## Pages in category "Rational Numbers"

The following 57 pages are in this category, out of 57 total.

### C

### F

### I

### O

### P

### R

- Rational Number can be Expressed as Simple Finite Continued Fraction
- Rational Number is Algebraic
- Rational Number is Algebraic of Degree 1
- Rational Number plus Irrational Number is Irrational
- Rational Numbers and Simple Finite Continued Fractions are Equivalent
- Rational Numbers are Countably Infinite
- Rational Numbers are Densely Ordered
- Rational Numbers are not Connected
- Rational Numbers are not Discrete Space
- Rational Numbers are Totally Disconnected
- Rational Numbers are Well-Orderable
- Rational Numbers form F-Sigma Set in Reals
- Rational Numbers form Field
- Rational Numbers form Integral Domain
- Rational Numbers form Metric Space
- Rational Numbers form Ordered Field
- Rational Numbers form Ordered Integral Domain
- Rational Numbers form Prime Field
- Rational Numbers form Ring
- Rational Numbers form Subfield of Complex Numbers
- Rational Numbers form Subfield of Real Numbers
- Rational Numbers form Subset of Real Numbers
- Rational Numbers form Vector Space
- Rational Numbers whose Denominators are not Divisible by 4 do not form Ring
- Rational Numbers with Denominator Power of Two form Integral Domain
- Rational Square Root of Integer is Integer
- Real Number is not necessarily Rational Number
- Ring Monomorphism from Integers to Rationals

### S

- Set of Rational Numbers is not Closed in Reals
- Set of Rational Numbers is not G-Delta Set in Reals
- Set of Rational Numbers Strictly between Zero and One has no Greatest or Least Element
- Set of Rationals Greater than Root 2 has no Smallest Element
- Set of Rationals Less than Root 2 has no Greatest Element
- Simple Finite Continued Fraction has Rational Value
- Smallest Strictly Positive Rational Number does not Exist