Set of Real Numbers

Set of Real Numbers Set – a collection of objects Real Numbers – Include both rational and

irrational numbers Natural Numbers – Numbers used for

counting (1,2,3,…) Whole Numbers – natural numbers with 0

included (0,1,2,3,…) Integers – Set of whole numbers and their

opposites (…,-4,-3,-2,1,0,1,2,3,4,…)

Sets

3x x is a natural number less than

The set of

All number x

such that

x is a natural number less than 3

Elements in a set

The members of a set are called its elements.

A set that contains no elements is called the empty set (or null set) symbolized by

32

The set

x x is amonthwith days is or

or

Rational and Irrational Numbers

Rational Numbers can be expressed as an integer divided by a nonzero integer

Irrational Numbers are numbers whose decimal representation neither terminates nor has a repeating block of digits. They cannot be represented as the quotient of two integers.

Examples of Rational Numbers

-5, 0, 9.45, 4

78.734,

Examples of Irrational Numbers

10, 3, , 7.161161116..., 3.491...

Given the following numbers…

20, 10, 5.34, 18.999,

11, 7, 2,

452

0, , 9.34334333433334...3

1. Name the natural numbers2. Name the whole numbers3. Name the integers4. Name the irrational numbers5. Name the rational numbers6. Name the real numbers

True or False?

a. 3 is a real numberb. is an irrational number

c. Every rational number is an integer

d. is a real number

1

5

Subsets

Subsets – sets contained within Ex: Every integer is also a rational

number. In other words, all the elements of the set of integers are also elements of the set of rational numbers. When this happens we say that the set of integers, set Z, is a subset of the set of rational numbers, set Q. In symbols,

Z Q

Symbols

used todenote that anelement is in a particular set

is read as is not anelement of

3 1,2,3,4,53 is an element of {1,2,3,4,5}

,5, , ,p a g j q

p is not an element of {a, 5, g, j, q}

List the elements in each set.

1 6

100

x x is a wholenumber between and

x x is a rational number greater than

Practice

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