JMAT_V2_N4_RP4 James E. Osler II Journal on Mathematics 2277-5137 2 4 21 32 Bijection, Categorical, Coextensive, Collaboration, Combinations, Complements, Coordinate, Equinumerosity, Equation, Exponent, Formula, Instrument, Integer, Investigation, Mathematical Model, Mathematics, Notation, Parallel, Positive, Proximal, Reflexivity, Research, Statistics, Symmetry, Table, Triangulation, Trichotomy, Tri–Squared, United, Unlimited, and Universal This monograph provides anepistemological rational for the mathematical “ProximalPositive ParallelNotation” as a novel mathematical operation. This innovative mathematical notation is used to define the relationship between values that construct the Standard Tri–Squared Test 3 × 3 Table used in the transformative process of qualitative data into quantitative outcomes. The Tri–Squared Test was introduced in an earlier Journal on Mathematics article by the author. The mathematical notion of “Unlimitation” is also introduced as an explicative part of the definition of the Proximal Positive Parallel formulae. Integrated into this new parallel notation is theneoteric “Coextensive” sign as a symbol of the relationship between terms. The Proximal Positive Parallel as a unique and inventive mathematical notation that may be applied to other areas and arenas of mathematics, statistics, and other sciences. Its broader application in diverse academic fields (such as the social sciences) will aid in building and strengthening the connections between mathematics and other academic disciplines. October - December 2013 Copyright © 2013 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=2612