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But your algebraic arithmetic with max-wise and min-wise characters is not equivalent at all! In fact it's a terrible analogy.

Bit-wise arithmetic is great because it's operations are compatible with propositional calculus,- but I cannot see how you can do anything productive with min/max-wise defined AND/OR for base10. For example how to do you determine 324 XOR 310 in your notation?




In this decimal digit context it would be appropriate to define

  NOT d = 9 - d
Similar to

  NOT b = 1 - b
for binary digits. And in fuzzy logic.

Taking the logic identity

  a XOR b = ( a AND NOT b ) OR ( NOT a AND b )
it would be

  MAX( MIN( a, NOT( b ) ), MIN( NOT( a ), b ) )




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