Download Number Sets

Number Sets
September 04, 2013
Number Sets
The set of real numbers, R
Q
Z
N
Ir
W
N (Natural Numbers) = {1, 2, 3, ...}
W (Whole Numbers) = {0} ∪ N = {0, 1, 2, 3, ...}
Z (Integers) = {..., ­3, ­2, ­1} ∪ W = {...,­3, ­2, ­1, 0, 1, 2, 3, ...}
a
Q (Rational Numbers) = A number expressed in the form where a and
b
b are integers and b is not equal to 0. The set of Integers is a subset of Rational Numbers.
Ir (Irrational Numbers) = A nonrepeating, nonterminating decimal.
R (Real Numbers) = Q ∪ Ir
Some Notation
∀ - "for all"
∃ - "There exists"
∈ - "an element of"
∴ - "therefore"
∨ - "or "
∧ - "and"
∪ - "union"
∩ - "intersect"
∅ - "the empty set"
Warm­up:
Tell whether each statement is true or false. Explain your answer.
T 1. Every counting number is a rational number.
T 2. Every whole number is an integer.
F 3. Every integer is a whole number.
T 4. The smallest whole number is 0.
T 5. Every rational number can be expressed as a repeating decimal.
T 6. Every repeating decimal is a rational number.
F 7. All integers are whole numbers.
T 8. Some integers are whole numbers.