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I'm looking for an example of a complete definition of a custom calculus I could learn from to mathematically correct define my own calculus consinsting of:

  • objects: a, aa, aaa, aaaa, aaaa, ... , b, bb, bbb, bbbb, etc
  • operations on those objects: + , - , *; eg: a+a = aa
  • etc...

Basically I want to remap natural numbers and the basic functions for my own needs and am looking for good resource to define a mathematically sound framework.

  • 5
    I think what you want to define is not a calculus, but an algebraic structure. Calculus is about differentiation and integration. Algebra is about adding and multiplying.2012-08-12
  • 4
    Look into abstract or universal algebra. Magmas, monoids, semigroups, groups, rings, semirings, fields, modules, preorders, posets, lattices, whatever your heart desires.2012-08-12
  • 7
    @celtschk: *Differential* calculus and *integral* calculus are about differentiation and integration.2012-08-12
  • 7
    Agreed - lets not forget that propositional calculus and predicate calculus have nothing to do with differentiation and integration.2012-08-12

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