An axiom, sometimes also known as a postulate, is a premise
which is accepted as true without proof. It differs from an act
of faith in that an axiom is typically either accepted "for the
sake of argument", or is simply "self-evident". A mathematical
system of logic seeks to prove statements, typically known as
theorems, by combining other statements according to the
inference rules defined as part of the logical system. In order
to "get started" in this process it is desirable to have
statements that don't need to be proved. These are the axioms.
(It is possible for a system of logic to have no axioms, but
most do.) For a specific example, suppose we want to devise a
system of logic to prove statements about arithmetic, we might
define rules of inference like - "if a is an integer, then a+1
is also an integer", and - "if a and b are both integers, and a
= b, then a+1 = b+1". But this does not get us very far unless
we also define some axioms as starting points — namely - 0 is an
integer, and - 0 = 0. By comb