| | = c
Binary operations on a set S (i.e., maps S S S )
Commutative, Associative Laws
Closure on a s/set.
Ex: Finite Fields
a. 1 is a number.
b. For each number n, there is another number n' called the successor of n.
c. For each number n, n' does not equal 1.
d. For all numbers m and n, if m' = n' then m = n.
e. Inductive Property: If a set S of numbers has the properties:
All models of Peano's Axioms are isomorphic.
Addition: Let n be a natural number. Then