Sia1e Ppt 0 2

Sets and Classification of Numbers Section R.2

Set Notation ,[object Object],C = {2, 4, 6, 8, 10} This method of representing a set is called the roster method . C represents the set. Braces are used to enclose the elements .

Set-Builder Notation ,[object Object],C = { x | x is an even digit} When a letter can be used to represent any digit, it is called a variable . Letters are used to represent numbers. The bar is read “such that.”

Set Notation ,[object Object],[object Object],[object Object],[object Object],[object Object]

Venn Diagrams ,[object Object],U = {0, 2, 4, 6, 8, 10} A = {2, 6} B = {0, 2, 6, 10} U B A The universal set contains all elements of interest.

Using Set Notation ,[object Object],[object Object],(a) B  A (b) B = C (c)  = C (d) A  B True. All elements in B are also in A . False. B and C do not have the same elements. True. The empty set is a subset of every set. False. There are elements in A that are not in B.

Classification of Numbers ,[object Object],The whole numbers are the numbers in the set W = {0, 1, 2, 3, …}. Ellipsis indicate that the pattern continues indefinitely.

Classification of Numbers ,[object Object],The set of rational integers are the numbers in the set A rational number is a number that can be expressed as a quotient of two integers. The integer p is called the numerator , and the integer q is called the denominator .

Rational Numbers ,[object Object],Rational numbers can also be represented as decimals. The decimal representation of a number is found by carrying out the division indicated. The repeat bar shows that the pattern continues. These decimals terminate .

Irrational Numbers ,[object Object],These decimals continue. Notice that if a number is rational, it cannot be irrational and vice-versa.

The Real Numbers Irrational numbers Rational numbers Integers Whole Numbers Natural Numbers

Classifying Numbers ,[object Object],[object Object],[object Object],(a) Counting numbers (b) Whole numbers (c) Integers (d) Rational numbers (e) Irrational numbers (f) Real numbers

Truncating Decimals ,[object Object],Example : Approximate 45.28502 to two decimal places by truncating. 45.28502 45.28

Rounding Decimals ,[object Object],Example : Approximate 45.28502 to two decimal places by rounding. 45.28502 45.29 The 5 tells us to add 1 to the final digit.

The Real Number Line ,[object Object],The distance between 0 and 1 determines the scale of the number line. The number associated with a point is called the coordinate . 2 – 2 0 1 3 4 5 – 1 – 3 – 4 – 5 Negative numbers Positive numbers Origin

Plotting Points Example : On the real number line, label the points with the coordinates 0, 1.75, – 2.5, 4. Real numbers are named in order on the number line. – 2.5 < 0 0 > 4 2 – 2 0 1 3 4 5 – 1 – 3 – 4 – 5 “ less than” “ greater than”

Ordering Numbers Example : Replace the ? With < , > or =. (a) 3 ? –2 Since 3 lies to the right of –2, we know that 3 > –2. (b) 3 ? 5.6 Since 3 lies to the left of 5.6, we know that 3 < 5.6. > < (c) – 2 ? Since – 2 is another way of writing we know that =

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