Math 340, Set Theory and Logic
Definitions
These are almost all of the definitions used in the course Math 340, Set Theory and Logic, with jason howald, Fall 2007. You
will be required to gradually memorize this entire document. Don’t panic – it’s easier than it sounds. Italized comments
need not be memorized.
(1) A mathematical theory is called universal if
(2) A set is
(3) We write x∈yto indicate
(4) For sets Aand B, we write A=Bto indicate
(5) For a set A, its cardinality, written |A|, is
(6) We write {e1, . . . , en}, (called list notation) to indicate
(7) We write {[variable things]; [conditions]}, (called set builder notation) to indicate
(8) We write Zfor
(9) We write ωfor
(10) We write Nfor
(11) We write Qfor
(12) We write Rfor
(13) For two sets Aand B, the union of Aand B, written A∪B, is
(14) For two sets Aand B, the intersection of Aand B, written A∩B, is
(15) For two sets Aand B, the set difference, written A\Bor A−Band pronounced “Awithout Bor “Aminus B” is
(16) For a set A, the complement of A, written Ac, is
(17) For two sets Aand B, we say Ais a subset of B, and write A⊆B, to mean
