# Tao Analysis Flashcards

Welcome! This website provides spaced repetition flashcards for Terence
Tao's *Analysis I*, via Orbit.
Flashcards look like this:

Orbit was intended to be used for online writing so that the reader can
do the flashcards as they are reading the text. Since *Analysis I* was
not written as an online text with embedded flashcards, the flashcards must
be hosted externally on this site. That means that you, the reader, will
need to do a little bit of extra work to remember to come back to this site
after reading each section of the book. The outline below is to help you know when to
do which set of flashcards. After you do a set of flashcards, reminder
emails will be sent to you so you will not need to keep visiting this
site. For more information, please see the Orbit
website.

## Schedule

- Chapter 1: Introduction
- No cards for this chapter.

- Chapter 2: Starting at the beginning: the natural numbers
- After reading section 2.1: The Peano Axioms (2.1), Peano axioms (optional)
- After reading section 2.2: Addition (2.2)
- After reading section 2.3: Multiplication (2.3)

- Chapter 3: Set theory
- After reading section 3.1: Fundamentals (3.1), Number of elements in sets
- After reading section 3.2: Russellâ€™s paradox (3.2)
- After reading section 3.3: Functions (3.3), Properties of the successor function
- After reading section 3.4: Images and inverse images (3.4)
- After reading section 3.5: Cartesian products (3.5)
- After reading section 3.6: Cardinality of sets (3.6)

- Chapter 4: Integers and rationals
- After reading section 4.1: The integers (4.1)
- After reading section 4.2: The rationals (4.2)
- After reading section 4.3: Absolute value and exponentiation (4.3)
- After reading section 4.4: Gaps in the rational numbers (4.4)

- Chapter 5: The real numbers
- After reading section 5.1: Cauchy sequences (5.1)
- After reading section 5.2: Equivalent Cauchy sequences (5.2)
- After reading section 5.3: The construction of the real numbers (5.3)