In mathematics, an algebraic model defines a set in terms of the operations that can be applied to it; their meaning is defined purely in terms of the equivalences that hold between different applications.

A set of entities, operations, and the equivalences that hold for them, is an algebra.

Some familiar equivalences:

  • (a+b)+c = a+(b+c)
  • (a+b)*c = (a+c)*(b+c)
  • a*1 = 1*a = a

A typical algebraic approach: the Peano axioms to define natural numbers.