# Symbols:Q

## Contents

## Set of Rational Numbers

- $\Q$

The set of rational numbers.

The $\LaTeX$ code for \(\Q\) is `\Q`

or `\mathbb Q`

or `\Bbb Q`

.

## Set of Non-Zero Rational Numbers

- $\Q_{\ne 0}$

The set of non-zero rational numbers:

- $\Q_{\ne 0} = \Q \setminus \left\{{0}\right\}$

The $\LaTeX$ code for \(\Q_{\ne 0}\) is `\Q_{\ne 0}`

or `\mathbb Q_{\ne 0}`

or `\Bbb Q_{\ne 0}`

.

## Set of Non-Negative Rational Numbers

- $\Q_{\ge 0}$

The set of non-negative rational numbers:

- $\Q_{\ge 0} = \set {x \in \Q: x \ge 0}$

The $\LaTeX$ code for \(\Q_{\ge 0}\) is `\Q_{\ge 0}`

or `\mathbb Q_{\ge 0}`

or `\Bbb Q_{\ge 0}`

.

## Set of Strictly Positive Rational Numbers

- $\Q_{> 0}$

The set of strictly positive rational numbers:

- $\Q_{> 0} = \set {x \in \Q: x > 0}$

The $\LaTeX$ code for \(\Q_{> 0}\) is `\Q_{> 0}`

or `\mathbb Q_{> 0}`

or `\Bbb Q_{> 0}`

.

## Probability

- $q$

Used in conjunction with the general probability $p$:

- $q = 1 - p$

As such, $q$ is a real number such that:

- $0 \le q \le 1$

and

- $p + q = 1$

The $\LaTeX$ code for \(q\) is `q`

.

## Quotient Mapping

- $q_\mathcal R$

The **quotient mapping induced by $\mathcal R$**:

- $q_\mathcal R: S \to S / \mathcal R: \map {q_\mathcal R} s = \eqclass s {\mathcal R}$

where:

- $\mathcal R \subseteq S \times S$ be an equivalence relation on a set $S$

- $\eqclass s {\mathcal R}$ is the $\mathcal R$-equivalence class of $s$

- $S / \mathcal R$ is the quotient set of $S$ determined by $\mathcal R$.

Also known as:

- the
**canonical surjection**from $S$ to $S / \mathcal R$ - the
**canonical map**or**canonical projection**from $S$ onto $S / \mathcal R$ - the
**natural mapping**from $S$ to $S / \mathcal R$ - the
**natural surjection**from $S$ to $S / \mathcal R$ - the
**classifying map**or**classifying mapping**(as it*classifies*the elements of $S$ into those various equivalence classes) - the
**projection**from $S$ to $S / \mathcal R$

The $\LaTeX$ code for \(q_\mathcal R: S \to S / \mathcal R\) is `q_\mathcal R: S \to S / \mathcal R`

.