# Symbols:Greek/Tau

## Tau

The $19$th letter of the Greek alphabet.

- Minuscule: $\tau$

- Majuscule: $\Tau$

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

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

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## Divisor Counting Function (Tau Function)

- $\map \tau n$

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

The **divisor counting function** is defined on $n$ as being the total number of positive integer divisors of $n$.

It is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ as $\tau$ (the Greek letter **tau**).

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 \(\map \tau n\) is `\map \tau n`

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## Topology

- $\tau$

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

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

## Linguistic Note

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