By I. N. Herstein
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Extra info for Abstract Algebra. Student's Solution Manual
Example text
3 ʦ (6, 7) 2 ᎏᎏ, 9 101. 0 ʦ (0, 1) 102. (0, 2) ʕ W 23 ᎏᎏ, 999 23 ᎏᎏ, 99 234 ᎏᎏ, 999 23 ᎏᎏ, and 9999 1234 ᎏᎏ. 9999 a) What do these decimals have in common? b) What is the relationship between each fraction and its decimal representation? 103. (0, 1) ʝ [1, 2] ϭ л 104. 3 In This Section 2 ᎏᎏ, 99 Operations on the Set of Real Numbers Computations in algebra are performed with positive and negative numbers. In this section, we will extend the basic operations of arithmetic to the negative numbers. U1V Absolute Value U2V Addition U3V Subtraction U4V Multiplication U5V Division U6V Division by Zero U1V Absolute Value The real numbers are the coordinates of the points on the number line.
I 42. 666 . . ʦ Q 43. ʦ I 44. ʦ Q Place one of the symbols ʕ, each statement is true. , ʦ, or W 46. Z Q 47. Z N 48. Q W 49. Q R 50. I 51. л I 52. л Q 53. N R 54. W R 55. 5 Z 56. Ϫ6 57. 7 Q 58. 8 61. 0 63. ͕2, 3͖ 65. ͕3, ͙2ෆ ͖ R 62. 0 I R 77. 3 4 5 6 7 8 9 78. 3 4 5 6 7 8 9 Q I Q 64. ͕0, 1͖ Q 76. The set of real numbers greater than 2 and less than or equal to 5. Write the interval notation for the interval of real numbers shown in each graph. Z 60. ͙2 ෆ R 75. The set of real numbers greater than or equal to 1 and less than 3 in each blank so that 45.
See Fig. 8. The numbers corresponding to the points on the line are called the coordinates of the points. The distance between two consecutive integers is called a unit, and it is the same for any two consecutive integers. The point with coordinate 0 is called the origin. The numbers on the number line increase in size from left to right. When we compare the size of any two numbers, the larger number lies to the right of the smaller one on the number line. 8 It is often convenient to illustrate sets of numbers on a number line.
