Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
P.1 Real Numbers Algebra III Real Number System Natural {1, 2, 3, 4,…} How many natural numbers are there? Real Number System Natural Whole What is the difference between natural and whole? How many whole numbers are there? {0, 1, 2, 3, 4,…} Is every whole number a natural number? Real Number System Natural Whole Integers {...-3, -2, -1, 0, 1, 2, 3, …} How many integers are there? Real Number System Natural Whole Integers Rational Fractions How many rational numbers are there? a a, b I , b 0 b Real Number System Natural Whole Integers Rational 2, , e How many irrational numbers are there? Irrational Real Number System Natural Whole Integers Each set is a subset of the Real Number System. The union of all these sets forms the real number system. The number line is our model for the real number system. Irrational Rational Real Numbers Interval Notation Example 1 x 5 3 5 5 x 2 Notice that the open circle translates into a parenthesis. We can also express this solution with a graph. -2 (2, ) A third way to express this solution is by using interval notation. Example 2 1 x 5 We can express this situation with a graph. -1 5 We can also express this graph with interval notation. (1, 5] Example 3 x 1 or x5 We can express this situation with a graph. -1 5 We can also express this graph with interval notation. (, 1] (5, ) Exercise 1 Translate the graph into interval notation. -3 5 [3, 5) Solid circles are brackets. Open circles are parenthesis. Exercise 2 Translate the graph into interval notation. 3 (3, ) Arrows translate into infinity signs with parenthesis. Always. Exercise 3 Translate the graph into interval notation. ( , ) Arrows translate into infinity signs with parenthesis. Negative infinity always goes to the left. Positive infinity always goes to the right. Exercise 4 Translate the graph into interval notation. -8 10 (, 8) (10, ) An open circles is always a parenthesis. Negative infinity always goes to the left. Positive infinity always goes to the right. P.1 Determine which numbers are (a) natural numbers, (b) integers, (c) rational numbers, and (d) irrational numbers. 7 2 9, ,5, , 2, 0,1, 4, 1 2 3 In exercises 25-34, (a) verbally describe the subset of real numbers represented by the inequality, (b) sketch the subset on the real number line and (c) state weather the interval is bounded or unbounded x4 In exercises 37 – 47, use inequality and interval notation to describe the set. p is less than 8 but no less than -1. P.1 Assignment • • • • • P.1 assignment page 9 1 – 5 all 25 – 34 37- 47 odd 97 – 101