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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) .



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.