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- Weak Mathematical Induction: If the following two things can be shown
about a proposition
:
- Base Case:
is true.
- Induction Step: If
is true, then
is true.
then
is true
.
- Strong Mathematical Induction: If the following two things can be shown
about a proposition
:
- Base Case:
is true.
- Induction Step: If
is true
,
, then
is true.
then
is true
.
- Pigeonhole Principle: If there are
pigeons and they are put in
pigeonholes, then there is a pigeonhole that contains at least two pigeons.
- Well Ordering Principle (WOP): If
is a non-empty set that is a
subset of the positive integers, then
has a least element.
- Transitivity: If
and
, then
.
- Substitution: If
, then
can be substituted for
in any statement
without changing the veracity(truthfulness) of the statement.
- Distributive Property:
.
Gregory Stoll
2000-04-08