# Part IA - Numbers and Sets

## Lectured by A. G. Thomason, Michaelmas 2014

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Proofs and logic
- 2 Sets, functions and relations
- 3 Division
- 4 Counting and integers
- 5 Modular arithmetic
- 5.1 Modular arithmetic
- 5.2 Multiple moduli
- 5.3 Prime moduli
- 5.4 Public-key (asymmetric) cryptography
- 6 Real numbers
- 6.1 Construction of numbers
- 6.2 Sequences
- 6.3 Series
- 6.4 Irrational numbers
- 6.5 Euler's number
- 6.6 Algebraic numbers
- 7 Countability