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Homework Assignment 7

Assigned Tuesday October 26; due Friday November 5, 2PM, at SS 1071

this document in PDF: HW.pdf

Required reading. All of Spivak's Chapter 7.

To be handed in. From Spivak Chapter 7: 1 (even), 2 (even), 10, 17.

Recommended for extra practice. From Spivak Chapter 7: 1 (odd), 2 (odd), 5, 11, 14.

Just for fun.

1. Can you ``add new numbers'' to the usual set ${\mathbb{R}}$ of real numbers so as to get a set which satisfies $P1$ through $P12$ yet in which ${\mathbb{N}}$ is bounded?

2. Player $A$ and player $B$ both have an unlimited supply of $1\times 1$, $1\times 2$, $1\times 4$, $2\times 2$ and $2\times 4$ Lego blocks. They alternate assembling them on a $157\times 157$ Lego base board, but only allowing for single layer construction -- so a player cannot place a block on top of a block that's already there. The first player that can't make a move loses. Whom would you rather be, player $A$ or player $B$?

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