Transcript Special Sets of Numbers

Special Sets of Numbers
Remember to Silence Your
Cell Phone and Put It In Your
Bag!
Mathematics was invented.
Numbers vs. numerals
The Set of Counting Numbers
or Natural Numbers
N = {1, 2, 3, 4, 5, . . . }
The Counting Process
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Say the names of the counting numbers
Name the numerals
Write the numerals
Count a number of objects
The Whole Numbers
W = {0, 1, 2, 3, 4, 5, . . . }
A whole number is the unique
characteristic embodied in each finite
set and all the sets equivalent to it.
2.1 p. 65
The Set of Integers
I = { . . . -3, -2, -1, 0, 1, 2, 3, . . . }
For every natural number n, there is a unique
number the opposite of n, denoted by –n, such that
n + -n = 0.
The set of integers, I, is the union of the set of
natural numbers, the set of the opposites of the
natural numbers, and the set that contains zero.
I = {1, 2, 3, …}  {-1, -2, -3 ...}  {0}
5.1 p. 249
The Set of Rational Numbers
Q = { a | a, b, ϵ I, b ≠ 0}
b
This textbook calls
a
b
a fraction.
Fractions are Rational Numbers!
Integers are Rational Numbers!
Whole Numbers are Rational Numbers!
6.1 p. 302
The Set of Rational Numbers
(cont.)
A decimal is a symbol that uses a
base-ten place-value system with tenths
and powers of tenths to represent a
number
A decimal is a rational number!
6.1 p. 207
Relationships Among these
Sets of Numbers
NWIQ
Q
I
W
N
6.5 p. 362
What numbers are not Rational
Numbers?
Every rational number can be expressed
as a terminating or repeating decimal.
Numbers which cannot be expressed
as either repeating or terminating
decimals are not rational numbers.
6.1 p. 310 & 6.5 pp. 359-362
The Set of Irrational Numbers
Real numbers which cannot be
expressed as either repeating or
terminating decimals.
Examples:
6.5 pp. 361-363
The Set of Real Numbers
R = {Rational Numbers} ⋃ {Irrational Numbers}
Note – The set of rational numbers and the
set of irrational numbers are disjoint sets.
(They have no elements in common.)
6.5 pp. 361-363
What numbers are not Real numbers?
_____________ numbers are not real
numbers.
Examples: