Foundations of mathemtics Flashcards
N
Natural numbers {1,2,3,…}
Z
The set of all integers {0,+-1,+-2,+-3,…}
Q
The set of all natural numbers
R
The set of all real numbers
C
The set of all complex numbers {a+bi | a,b c R}
|u|
Number of elements in the set u
Singleton
A set with one element
∅
The empty set
What is a PROPER SUBSET
Every element of B is also an element of a but b does not equal A
[a,b]
x is greater or equal than a, and less than or equal to b.
(a,b)
x is greater than a and less than b.
AUB
Union, x is an element of a or an element of b
A∩B
Intersection, x is an element of A and of B
A\B
Difference, x is an element of A but not an element of B
Disjoint
When A and B have no common elements
The ordered N-tuple
(x1,x2,x3,…xn) where the position of each element is significant
What is the cartesian product of AxB
{(a,b) | a∈A and b∈B}
The principle of the excluded third
either P is true, or ˜P is true, there is no third possility
Disjunction
P or Q (or in an inclusive sense)
Conjunction
P and Q
∀
for every, for all
∃
there exists
Contrapositive
if P imlies Q, it’s contrapositive is that thee negation of P implies th negation of Q
1+2+3+….+n=?
n(n+1)/2
Image
The image of a function mapping A to B, is the set B
Domain
The domain of a function mapping A to B, is the set A
Injective
If a1,a2 are elements of A and a1->b and a2->b then a1=a2
one to one function
surjective
If f maps A to B every element of B is the image of at least one element of A
Bijective
A bijective function is both Injective and surjetive
Comutative
xy=yx
asociative
x(yz)=(xy)z etc
Identity element
ex=xe=x (where e is the identity)
Inverse
if xy=yx=e then y is the inverse of x
