Hybrid Notation

mixes boundary structure with special symbols that stand in place of specific boundary forms.

Usually these special symbols are reminiscent of conventional notations. Special symbols will be necessary in order to make the upcoming boundary forms of π, i, cosine, and the like easier to read. A hybrid notation makes unfamiliar forms a bit more readable. It is particularly handy when the same boundary pattern occurs multiple times within a Form.

The archetypical special symbol is the variable A, which stands in place of any James form. Naming boundary structures is safe so long as unique names are assigned to unique patterns. And of course we can conveniently move back and forth between a name and the form that the name identifies. We can also engage in symbolic abbreviations for both typographical and reading convenience. We’ll sometimes use natural numbers, for example, to stand in place of ensembles of units. It will be convenient to use the special symbol “5”, for example, to stand in place of the form ooooo. Sometimes however it is conceptually important to show these ensembles explicitly.

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Bricken, Iconic Arithmetic Volume I, p. 147.