Example 1.1. Use a calculator to approximate Ï} 6 to the nearest tenth: Ï} 6 ø . 1.4. A number line is an easy method of picturing the set of real numbers. The Ordered Field Properties of the Real Numbers 90 5. See also: This was the first manifestation of one of the truly powerful properties of complex numbers: real solutions of real problems can be determined by computations in the complex domain. The Real Numbers are characterized by the properties of Complete Ordered Fields. Mathematical Induction 91 Appendix B. Whole Numbers : (same as , but throw in zero) 3. We will use the notation from these examples throughout this course. Properties and Operations of Fractions Let a, b, c and d be real numbers, variables, or algebraic expressions such that b ≠ 0 and d ≠ 0. 1.2_Notes_Honors_Algebra_2.pdf - 1.2 Properties of Real Numbers HW p 14 required#19 23-31odd 35 39 41 45 47 49 55 59 61 71 73 75 optional#21 33 37 43 51 which we calculate first) (a + b) + c = a + (b + c) 3. 24 23 22 21 210 3 4 Example 1 Graph real numbers on a number line a2_mnlaect353043_c01l01-07.indd 1-1 9/16/09 7:16:39 PM 1.1 Euclid’s GCD algorithm Given two positive integers, this algorithm computes the greatest common divisor (gcd) of the two numbers. erties persist. Adding zero leaves the real number unchanged, likewise for multiplying by 1: Identity example. VII given any two real numbers a,b, either a = b or a < b or b < a. Two whole numbers add up to give another whole number. The ordering < is compatible with the arithmetic operations means the following: VIII a < b =⇒ a+c < b+c and ad < bd for all a,b,c ∈ R and d > 0. 1 Thus the equivalence of new objects (fractions) is deflned in terms of equality of familiar objects, namely integers. [a;b) is the set of all real numbers xwhich satisfy a x> < >>: x if x 0 x if x<0 Note. Graph the real numbers 2} 13 and 5 Ï} 6 on a number line. Below are some examples of sets of real numbers. Properties of Whole Numbers. Cardinality 93 2. 4x3 y5 = Power Property: Multiply exponents when they are inside and outside parenthesis EX w/ numbers: (53)4 = EX w/ variables: (y3)11 = EX w/ num. Two fundamental partial order relations are the “less than or equal to (<=)” relation on a set of real numbers and the “subset (⊆⊆⊆⊆)” relation on a set of sets. A.N.1: Identifying Properties: Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) 1 Which property is illustrated by the equation ax+ay =a(x+y)? Examples: ½ -¼ 0.19 4.27 31 The irrational numbers are numbers that cannot be written as an integer divided by an integer. Open and Closed Sets 96 … Property Commutative Associative Identity Inverse Closure Distributive a (b + c) = ab + acand (b + = ba+ ca Rational numbers can be expressed as a ratio g where a and b are integers and b is not zero. a+b is real 2 + 3 = 5 is real. long division and in the theory of approximation to real numbers by rationals. 2. SWBAT: identify and apply the commutative, associative, and distributive properties to simplify expressions 4 Algebra Regents Questions 1) The statement is an example of the use of which property of real numbers? The Field Properties of the Real Numbers 85 3. Sets A set is a list of numbers: We separate the entries with commas, and close off the left and right with and . Number Systems Notes Mathematics Secondary Course MODULE - 1 Algebra 3 1 ... illustrate the extension of system of numbers from natural numbers to real (rationals and irrational) numbers. 2 – 11) Topics: Classifying numbers, placing numbers on the number line, order of operations, properties I. The collection of all real numbers between two given real numbers form an interval. A. ab = ba B. a(bc) = (ab)c C. a(b+c) = ab+ac D. a1 = a 2.
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