# Symbols:Greek/Tau

## Contents

## Tau

The $19$th letter of the Greek alphabet.

- Minuscule: $\tau$

- Majuscule: $\Tau$

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

.

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

.

### Tau Function

- $\tau \left({n}\right)$

Let $n$ be an integer such that $n \ge 1$.

The **$\tau$ (tau) function** is defined on $n$ as being the total number of positive integer divisors of $n$.

That is:

- $\displaystyle \map \tau n = \sum_{d \mathop \divides n} 1$

where $\displaystyle \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.

The $\LaTeX$ code for \(\tau \left({n}\right)\) is `\tau \left({n}\right)`

.

## Topology

- $\tau$

Frequently used, and conventionally in many texts, to denote a general topology.

It is usually introduced as part of the notation $T = \left({S, \tau}\right)$ for a general topological space.

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

.

## Linguistic Note

The name of the Greek letter $\tau$ (tau) is properly pronounced to rhyme with **cow** not **caw**.