Tuesday, August 8 2000
Quiz 9
Name: _______________________________
Georg Cantor (1845-1918)
No two different elements of the set A are mapped to the same element
in B.
"forall x exists y ( x < y )" is true if for all numbers there exists
a greater number. This can be true only with infinite sets and
it certainly the case for the natural numbers.
"exists x forall y ( x < y )" is true if there is one number such that
all numbers are greater than it. This sentence is false, since
no number is greater than itself. If would be true if the
relation were "greater or equal", because in this case there is a
number such that all numbers are greater or equal, namely 1.
Intuitionistic logic, Modal logic, Linear logic, Fuzzy logic, etc.
(a) A base
clause, which defines the basic elements of the set.
(b) One
or more inductive clauses: they tell us
how to generate complex elements from parts.
(c) And a final clause which states that all
elements are either basic elements or generated by the inductive clause.