Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I:

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Homework Assignment 5

Assigned Tuesday October 8; due Friday October 18, 2PM at SS 1071

this document in PDF: HW05.pdf

Required reading

All of Spivak Chapter 6.

To be handed in

From Spivak Chapter 6: 1(i)-(iii), 3, 12, 14

Recommended for extra practice

From Spivak Chapter 6: 1(iv), 4, 10, 13, 16 parts (a) through (c).

Just for fun

Solve Spivak's problem 16 parts (d) and (e) and also the following problem:

Problem. Could there be a non-constant continuous function defined on the entire ``unit'' interval $[0,1]$, which is constant on certain open subintervals of $[0,1]$ whose total length is exactly equal to $1$? (Obviously, I wouldn't be asking this question if the answer wasn't $\underline{\qquad}$).

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