# Symbols:Greek/Tau

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## 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 .

## 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 .

## 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.