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[107x583]Chapter 2
[107x533]Mathematical Induction:
[107x503]"And so on . . . "
[107x444]2.1 Introduction
[107x421]This chapter marks our first big step toward investigating mathematical proofs
[107x410]more throughly and learning to construct our own. It is also an introduction
[107x398]to the first significant
[107x398]proof technique
[209x398]we will see. As we describe below,
[107x386]this chapter is meant to be an appetizer, a first taste, of what
[107x386]mathematical
[107x374]induction
[107x374]is and how to use it. A couple of chapters from now, we will we be
[107x362]able to rigorously define induction and
[107x362]prove
[278x362]that this technique is mathemati-
[107x350]cally valid. That's right, we'll actually prove how and why it works! For now,
[107x338]though, we'll continue our investigation of some interesting mathematical puz-
[107x326]zles, with these particular problems hand-picked by us for their use of inductive
[107x314]techniques.
[107x283]2.1.1 Objectives
[107x264]The following short sections in this introduction will show you how this chapter
[107x252]fits into the scheme of the book. They will describe how our previous work
[107x240]will be helpful, they will motivate why we would care to investigate the topics
[107x228]that appear in this chapter, and they will tell you our goals and what you
[107x216]should keep in mind while reading along to achieve those goals. Right now,
[107x204]we will summarize the main objectives of this chapter for you via a series of
[107x192]statements. These describe the skills and knowledge you should have gained by
[107x180]the conclusion of this chapter. The following sections will reiterate these ideas
[107x168]in more detail, but this will provide you with a brief list for future reference.
[107x156]When you finish working through this chapter, return to this list and see if you
[107x144]understand all of these objectives. Do you see why we outlined them here as
[107x132]being important? Can you define all the terminology we use? Can you apply
[107x120]the techniques we describe?
[271x95]101
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