SET:
Definition
A set is a collection of objects thought of as a whole.
• Describe a set by enumeration: list all the elements of the set e.g.
S = {2, 46, 8, 10} ={4, 10, 6, 2, 8}
• Describe a set by property:
State the property shared by all the elements in the set,
E.g. S = {x: x is an even number between 1 and 11}
ELEMENT OF SET:
If all the elements of a set X are also elements of a set Y, then X is a subset
Of Y: X ⊆ Y
Example 2.
• {4, 8, 10} ⊆ {2, 4, 6, 8, 10}
• {2, 4, 6, 8, 10} ⊆ {2, 4, 6, 8, 10}
If all the elements of a set X are also elements of a set Y, but not all the
Elements of Y are in X, then X is a proper subset of Y: X ⊂ Y
Two sets X and Y are equal if they contain exactly the same elements:
X = Y
Universal Set:
The set contains all possible objects under consideration, i.e. set U.
. The empty set:
This set is the set with no elements:
INTERSECTION:
A ∩D =; the intersection of the two sets X and Y is the set of elements that are n. The empty set is the set with no elements:
. A set with only one element is a singleton.
Union set,
The union of two set X and Y is the set of elements in one or the other of
the sets.
Natural numbers:
N = {1, 2, 3...} (Arise naturally from counting objects).Natural numbers: N = {1, 2, 3...} (Arise naturally from counting objects).
Integers:
I = {..., −3, −2, −1, 0,1,2,3...}
• closed under addition, subtraction, multiplication, but not division.
Rational numbers:
that every integer and the friction which can be written in the form {p/q}
integer and the friction Q = {a, b}
• Infinitely
many rational numbers between any two integers, e.g., 1 and 2:
Irrational numbers:
Numbers that cannot be expressed as ratios of integers. E.g.
(Between 1 and 2, not rational).
Real numbers (R):
Real numbers are those number that includes rational and irrational numbers.
