# properties of real numbers notes pdf

a + 0 = a 6 + 0 = 6. a × 1 = a 6 × 1 = 6 Properties of Whole Numbers. The empty set is the set containing nothing: . Write an example to demonstrate it. A. ab = ba B. a(bc) = (ab)c C. a(b+c) = ab+ac D. a1 = a 2. [a;b) is the set of all real numbers xwhich satisfy a x> < >>: x if x 0 x if x<0 Note. 1.1 Euclid’s GCD algorithm Given two positive integers, this algorithm computes the greatest common divisor (gcd) of the two numbers. Mathematical Induction 91 Appendix B. Examples: ½ -¼ 0.19 4.27 31 The irrational numbers are numbers that cannot be written as an integer divided by an integer. The Ordered Field Properties of the Real Numbers 90 5. Real Number Properties For any real numbers a, b, and c. Multiplication —a— a. bis a real number. (that is, the set Shas a least upper bound which is a real number). Which sentence is an example of the distributive property? The rational numbers are numbers that can be written as an integer divided by an integer (or a ratio of integers). 8S R and S6= ;, If Sis bounded above, then supSexists and supS2R. 4 NOTES ON REAL NUMBERS De nition 3. Abstract. The chart below is nice because it shows the addition and multiplication properties side by side do you can see the similarities and differences. Here, we will learn properties of whole numbers on the basic arithmetic operations like addition, subtraction, multiplication, and division. Addition a + b is a real number. a. rational numbers b. real number c. real numbers d. integers 2. The properties of whole numbers are given below. The following notation is used (a;b) is the set of all real numbers xwhich satisfy a