FHMM1014 Algebra Centre For Foundation Studies Department of Sciences and Engineering Contents 1.1 Real Numbers System 1.2 Indices and Logarithm FHMM1014 Mathematics I Chapter 1 Number and Set FHMM1014 Mathematics I 1 1.3 Complex Numbers 1.4 Set FHMM1014 Mathematics I 2 Real Numbers 1.1 Real Numbers • Let’s review the types of numbers that make up the real number system. FHMM1014 Mathematics I 3 FHMM1014 Mathematics I 4 1 FHMM1014 Algebra Real Numbers i) Natural numbers (also called positive integers). N = {1, 2, 3,…..} ii) Integers Natural numbers, their negatives and zero. Z = {……., -3, -2, -1, 0, 1, 2, 3, 4…….} Real Numbers iii) Rational numbers are ratios of integers. • Thus, any rational number • can be expressed as: Q m n where m and n are integers and n ≠ 0. FHMM1014 Mathematics I 5 FHMM1014 Mathematics I 6 Real Numbers Examples are: Real Numbers If a number is rational, then its corresponding decimal representation is either terminating or non-terminating repeating. 1 3 3 7 36 0.17 17 100 FHMM1014 Mathematics I 7 FHMM1014 Mathematics I 8 2 FHMM1014 Algebra Real Numbers For example 1 0.5 (terminating) 2 2 0.66666.... 0.6 (non terminating repeating) 3 (the bar indicates the digit repeat forever) 9 1.285714285714.... 1.285714 (non terminating repeating) 7 FHMM1014 Mathematics I 9 FHMM1014 Mathematics I Real Numbers There are also real numbers, such as that cannot be expressed as a ratio of integers. 2 , Hence, they are called irrational numbers. • Other examples are: 5 3 7 2 3 10 Real Numbers If the number is irrational, the decimal representation is non-terminating non-repeating: Real Numbers 5 2.236067978... 3.141592654... FHMM1014 Mathematics I 11 FHMM1014
