Talk:PlanetPhysics/Sole Sufficient Operator

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%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: sole sufficient operator %%% Primary Category Code: 02. %%% Filename: SoleSufficientOperator.tex %%% Version: 1 %%% Owner: Jon Awbrey %%% Author(s): Jon Awbrey %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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A \textbf{sole sufficient operator} or a \textbf{sole sufficient connective} is an \htmladdnormallink{operator}{http://planetphysics.us/encyclopedia/QuantumSpinNetworkFunctor2.html} that is sufficient by itself to define all of the \htmladdnormallink{operators}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} in a specified set of operators.

In logical contexts this refers to a logical operator that suffices to define all of the \htmladdnormallink{boolean-valued functions}{http://planetphysics.us/encyclopedia/Predicate.html}, $f : X \to \mathbb{B}$, where $X$ is an arbitrary set and where $\mathbb{B}$ is a generic 2-element set, typically $\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \}$, in particular, to define all of the finitary \htmladdnormallink{boolean functions}{http://planetphysics.us/encyclopedia/Predicate.html}, $f : \mathbb{B}^k \to \mathbb{B}$.

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