I using the term 'function' to mean a transformation of symbols, whereas a 'math function' would be a subset of the more general 'function' which, conceptually speaking, takes one input string and returns one output string of symbols.
I'm struggling to create a mapping of all functions to all strings. That is to say, I'm attempting to give each function a name, preferably a semantic name, where similar names respect similar acting / similarly constituted functions.
Here's one way I'm currently attempting to do this, but I'm not sure if it is the right approach (for instance identical functions; those that map identical inputs to outputs in this approach do have differing representations since they are differently constituted):
I'm aware that all other logic gates can be produced by combinations of nand and nor logic gates. Therefore all computation, and therefore all functions can be expressed in a binary series representing nand and nor respectively. Would using this representation of computation work to define all functions as each being a unique binary series?
Now, I'm not certain this hasn't been done before or if such an endeavor falls under a certain discipline. Any direction or help you could give me would be appreciated.
Well not necessarily NAND /NOR/AND/OR as finite operators .
Philosophically , Aristotle's postulates are wider, I hope condition to realizing the mapping functions. Again should be unique on the zeroth plane.
Article Logical Form and LF
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