# Symbols:Greek/Nu

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## Nu

The $13$th letter of the Greek alphabet.

Minuscule: $\nu$
Majuscule: $\Nu$

The $\LaTeX$ code for $\nu$ is \nu .

The $\LaTeX$ code for $\Nu$ is \Nu .

### Nu Function

$\map \nu n$

The $\nu$ function is the function $\nu: \Z_{>0} \to \Z_{>0}$ is defined as:

$\forall n \in \Z_{>0}: \map \nu n =$ the number of types of group of order $n$

The $\LaTeX$ code for $\map \nu n$ is \map \nu n .

### Minimal Negation Operator

$\nu_k$

Let $\Bbb B$ be a Boolean domain:

$\Bbb B = \set {\F, \T}$

The minimal negation operator $\nu$ is a multiary operator:

$\nu_k: \Bbb B^k \to \Bbb B$

where:

$k \in \N$ is a natural number
$\nu_k$ is a boolean function defined as:
$\map {\nu_k} {x_1, x_2, \ldots, x_k} = \begin {cases} \T & : \exists! x_j \in \set {x_1, x_2, \ldots, x_k}: x_j = \F \\ \F & : \text {otherwise} \end{cases}$

That is:

$\map {\nu_k} {x_1, x_2, \ldots, x_k}$ is true if and only if exactly one of its arguments is false.

The $\LaTeX$ code for $\nu_k$ is \nu_k .

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