Thursday, April 18, 2001
Quiz 10
Name: _______________________________
Georg Cantor (1845-1918)
The modern axioms of set theory, due to Zermelo and Fraenkel.
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.