Set of Real Numbers

1. Set of Real Numbers

2. 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,…)

3. Sets such that The set of x is a natural number less than 3 All number x

4. 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

5. 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.

6. Examples of Rational Numbers • -5, 0, 9.45,

7. Examples of Irrational Numbers

8. Given the following numbers… • Name the natural numbers • Name the whole numbers • Name the integers • Name the irrational numbers • Name the rational numbers • Name the real numbers

9. True or False? • 3 is a real number • is an irrational number • Every rational number is an integer • is a real number

10. 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,

11. Symbols 3 is an element of {1,2,3,4,5} p is not an element of {a, 5, g, j, q}

12. List the elements in each set.

13. Practice • Page 16 - #37 – 52 • Page 17 - #59 -91