The algebraic style of Boundary Math includes maintaining equality by transforming containment relations that match clearly defined patterns. If a containment pattern does not match a rule, then it cannot be changed. More generally the Axiomatic Principle constrains what can be done within a formal system.
of James algebra, the transformations that are designed to define the behavior of the arithmetic and algebra of numbers.
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This was an amazing innovation which applied a Mixture of Algebra and Geometry to the study of language, that is, language in its role as the medium of argumentation.