3. Let a and b be two unequal numbers from R. A. The difference ba is not necessarily positive. Explain. B. The absolute value b - al is necessarily positive, and (assuming that b lies to the right of a on the number line) the resulting value is frequently called the width of the interval (a, b). Thinking visually in terms of a horizontally-oriented number line, explain why this choice of words makes sense. C. (Henceforth, assume b lies to the right of a on the number line.) The real number a+b is frequently called the midpoint of the interval (a, b). Thinking visually in terms of a horizontally-oriented number line, explain why this choice of words makes sense.
3. Let a and b be two unequal numbers from R. A. The difference ba is not necessarily positive. Explain. B. The absolute value b - al is necessarily positive, and (assuming that b lies to the right of a on the number line) the resulting value is frequently called the width of the interval (a, b). Thinking visually in terms of a horizontally-oriented number line, explain why this choice of words makes sense. C. (Henceforth, assume b lies to the right of a on the number line.) The real number a+b is frequently called the midpoint of the interval (a, b). Thinking visually in terms of a horizontally-oriented number line, explain why this choice of words makes sense.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Let \( a \) and \( b \) be two unequal numbers from \( \mathbb{R} \).
A. The difference \( b - a \) is not necessarily positive. Explain.
B. The absolute value \(|b - a|\) is necessarily positive, and (assuming that \( b \) lies to the right of \( a \) on the number line) the resulting value is frequently called the width of the interval \( (a, b) \). Thinking visually in terms of a horizontally-oriented number line, explain why this choice of words makes sense.
C. (Henceforth, assume \( b \) lies to the right of \( a \) on the number line.) The real number \(\frac{a+b}{2}\) is frequently called the midpoint of the interval \( (a, b) \). Thinking visually in terms of a horizontally-oriented number line, explain why this choice of words makes sense.
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