Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I:

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Homework Assignment 5

Assigned Tuesday October 7; due Friday October 17, 2PM, at SS 1071

This document in PDF: HW.pdf

Required reading. All of Spivak Chapter 5.

To be handed in. From Spivak Chapter 5: 1 (odd parts), 3 (odd parts), 13, 21, 37.

Recommended for extra practice. From Spivak Chapter 5: 1 (even parts), 3 (even parts), 14, 24, 26.

Just for fun. Are there irrational numbers $a$ and $b$ so that $a^b$ would be rational? Can you find irrational numbers $a$ and $b$ so that $a^b$ would be rational?

Notice that these are two questions and not one. There is some interesting tale on the philosophy of mathematics for which this is a prime example; have your professor tell you about it some day between XX:00AM and XX:10AM.

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