Mathematics PDF
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MSc. Abdalameer Alrubaiee
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This document covers intervals, inequalities, and absolute values in mathematics. It includes examples and explanations of these concepts.
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Chapter One 1-1 Intervals A subset of the real line is called an interval if it contains at least two numbers and contains all the real numbers lying between any two of its elements. Table 1-1 shows types of intervals. 25-Mar-20...
Chapter One 1-1 Intervals A subset of the real line is called an interval if it contains at least two numbers and contains all the real numbers lying between any two of its elements. Table 1-1 shows types of intervals. 25-Mar-20 MSc. Abdalameer Alrubaiee 1 1-2 Inequalities: Rules for Inequalities If a, b, and c are real numbers, then: Notice the rules for multiplying an inequality by a number. Multiplying by a positive number preserves the inequality; multiplying by a negative number reverses the inequality. Also, reciprocation reverses the inequality for numbers of the same sign. For example, 2 < 5, -2 > -5 also 1/2 > 1/5. 1-3 Absolute Value The absolute value of a number x, denoted by ǀ x ǀ , is defined by the formula 𝑥, 𝑥≥0 𝑥 = −𝑥, 𝑥
