theory quiz Flashcards
a ‘is in” b symbol
not defined
A is a subclass of B symbol
A “symbol” B -> for all x:x in A -> x in B
empty set symbol
{} = {x:x not equal to x}
{a,b}
{x: x=a v x=b}
{a}
{x:x=a}
{a1, a2…an}
{x: x=a1 v x=a2…}
UA
{x:x in y for some y in A}
AUB
U{A,B}
nA
{x:x in y for all y in A}
AnB
n{A,B}
(a,b)
{{a},{b}}
(a1…an)
((a1…an-1), an)
AxB
{(a,b): a in A ^ b in B}
A1x…An
{(a1…an): ai in Ai for a=1…n}
PA
{x: x subclass A}
A^c
{x:x not in a}
A\B
{x:x in A ^ x not in B}
Function
in f and in f, then y=z
relation
binary relation R on A is a subset of AxA
dom f
{x:(x,y) in f for some y}
axiom of extensionality
A=B iff (for all x x in A iff x in B)
axion of empty set
The empty set is a set
axiom of pairing
for all objects a,b the class {a,b} is a set
axiom of subset
if B subclass A and A is a set, then B is a set
axiom of union
If A is a set, then UA is a set
axiom of power
If A is a set, then PA is a set
axiom of infinity
There exists z a set s.t. the empty set is in z and if a in z, then au{a} in z
axiom of replacement
if f is a function, if dom f is a set, then ran f is a set
axiom of choice
Cartesian product of a collection of non-empty sets is non-empty
ran f
{fx:x in dom f}
f:A->B
f is a function with A=domf ranf subclass of B
f(x)
f is a function, x in dom f and (x, f(x)) in f
Ui Ai
union of all sets Ai indexed by I=Uf[I]
ni Ai
n{Ai: i in I}
{x in A: P(x)}
set of all elements of A satisfying property P
