**Problem Statement:**(4) Prove that there is no smallest positive real number.**Explanation:**This statement is asking us to demonstrate why it is impossible to identify a smallest positive real number. The proof involves understanding the properties of real numbers and the concept of limits. Here's a common approach for the proof:**Proof:**1. **Assumption**: Assume, for the sake of contradiction, that there is a smallest positive real number, denoted by \( x \).2. **Contradiction**: Consider the number \( \frac{x}{2} \). This number is positive and clearly less than \( x \) because \( \frac{x}{2} < x \).3. **Conclusion**: Our assumption that \( x \) is the smallest positive real number leads to a contradiction since we've found a smaller positive real number \( \frac{x}{2} \). Therefore, no smallest positive real number exists. This example illustrates the density property of real numbers: between any two real numbers, another real number exists. Thus, no smallest positive real number can exist.

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Description: **Problem Statement:**(4) Prove that there is no smallest positive real number.**Explanation:**This statement is asking us to demonstrate why it is impossible to identify a smallest positive real number. The proof involves understanding the properti

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Math

Advanced Math

(4) Prove that there is no smallest positive real number.

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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