In
mathematics, a
proof is a series of
statements ordered in such a way so as to show that something is
true without
exception. There have been many
false proofs over the years (most notably,
Fermat's Last Theorem and
1=2), but there have also been new and
correct proofs recently (again,
Fermat's Last
Theorem).
Some of the first proofs were made by
Euclid and deal in
Euclidean Geometry. Other early theorems include the
Pythagorean Theorem and the
Chinese Remainder Theorem, although many of the "old" theorems were not proven satisfactorily until recently.
Most mathematical proofs are based in
logic and depend on
implications,
inverses,
converses and
contrapositives. Often, the most desirable kind of implication is the
iff statement. Every proof must be founded on
axioms or
definitions, statements which cannot be proven by any means but which can be
assumed true. In
fact, an axiom can be changed and there can still be logical
consistency in many cases;
compare Euclidean geometry with
non-Euclidean geometry and their
basic but
mutually exclusive axioms: "
Parallel lines never meet"; "Parallel lines meet at
infinity".
Some items which have proofs here:
Please /msg me with others.