Book contents
- Frontmatter
- Contents
- USES OF INFINITY
- Preface
- Chapter 1 Popular and Mathematical Infinities
- Chapter 2 From Natural Numbers to √2
- Chapter 3 From √2 to the Transfinite
- Chapter 4 Zig-Zags: To the Limit if the Limit Exists
- Chapter 5 The Self Perpetuating Golden Rectangle
- Chapter 6 Constructions and Proofs
- Solutions to Problems
- Bibliography
Solutions to Problems
- Frontmatter
- Contents
- USES OF INFINITY
- Preface
- Chapter 1 Popular and Mathematical Infinities
- Chapter 2 From Natural Numbers to √2
- Chapter 3 From √2 to the Transfinite
- Chapter 4 Zig-Zags: To the Limit if the Limit Exists
- Chapter 5 The Self Perpetuating Golden Rectangle
- Chapter 6 Constructions and Proofs
- Solutions to Problems
- Bibliography
Summary
CHAPTER TWO
2.1 This is a non-terminating sequence of sets of musical compositions, the first set consisting of compositions for one voice part or instrument, the second set of pieces for two performers, the third of pieces for three performers, and so on.
2.2 This is a periodic sequence of the four classes of hits in baseball. The iteration dots indicate that we are to repeat the same sequence of classes again and again.
2.3 Collections of siblings born on the same day make up the terms of this sequence. The first term is the collection of all individuals with one such sibling, the second is the set of individuals with two such siblings, etc. The terms which occur beyond a certain point in this infinite sequence are empty sets.
2.4 Here we have a list of the names of the days of the week. In this case the iteration dots represent an abbreviation for the days Saturday and Sunday.
2.5 This is a periodic sequence, the terms of which are the first letters in the names of the days of the week, in the order of the days, beginning with the letter M corresponding to Monday. The first term occurs again after six more terms, and from then on the entire period is repeated over and over.
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- Uses of Infinity , pp. 121 - 149Publisher: Mathematical Association of AmericaPrint publication year: 1962