
Set
 A "Set" is a collection of objects. We use the symbols {} to indicate that the collection is a set.
 Example:
 N = {1, 2, 3, 4, 5, . . . .}

Element
 An element is a member of a set. We use the symbol ϵ (is an element of) to indicate when an element belongs to a set.
 Example:
 3 ϵ {1, 2, 3, 4, 5, . . . }

What does each symbol look like?
Set =
Element =
Natural#'s =
Whole #'s =
Intagers =
Rational #'s =
 Set = {}
 Element = ϵ
 Natural#'s = N
 Whole #'s = W
 Intagers = I
 Rational #'s = Q

N =
 N = Natural #'s or
 {1, 2, 3, 4, 5, 6, . . . }

W =
 W = Whole #'s or
 {0, 1, 2, 3, 4, 5, 6, . . . .}

I =
 I = Intagers or
 {. . .3, 2, 1, 0, 1, 2, 3, . . .}

Q =
 Q = Rational #'s or repeating/ending decimal value, or any fraction with intagers. Infanetly many points between to points.
 Example:
 Q={a/ba ϵ I and b ϵ I and b ≠ 0}

Welldefined set
 A set is welldefined if we are able to tell whether any particular object is an element of the set.
 Note: Q > I > W > N


Universal set
The universal set is the set of all elements under consideration in a given discussion. We often denote the universal set by the capital letter U.

Subset
The set A is a subset of the set B if every element of A is also an element of B.

Proper subset
The set A is a proper subset of the set B if A B but A ≠ B.


Finite set
 The number of subsets of a finite set can be found by finding the cardinal number of the set. A set that has k elements has 2^{k} subsets.
 Example:
 A={(HH),(HT), (TH),(TT)} the set is finite and n(A) = 4. therefore 2^{4} = 16 subsets.
 Note: Pascals triangle to find subsets.

Cardinal #:
The Cardinal number is k in the finite set, or in other words, it is the total number of elements in the list.

Equivalent Sets
 Sets A and B are equivalent, or in OnetoOne correspondence, if n(A) = n(B).
 Example:
 A={1, 2, 3, 4} ; B={a, b, c, d} then A and B are equivalent.

