In mathematics, an algebra
ic model defines a set in terms of the operation
s that can be applied to it;
their meaning is defined purely in terms of the equivalence
s 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.