By Thomas Schaffter
- Category: Mathematics, Textbooks
- Type: ebook
- Release Date: 2012-08-31
- File Size: 5.70MB
- Developer: Thomas Schaffter
- App Ratings: 4/5 (19 App Reviews)
- Price: Free
Infinite Sets Details
The theory of infinite sets is my favorite subject in mathematics. The results are very counterintuitive - where would you get intuition about infinite things? As such, they are quite delightful; at least they are to me. This is a theoretical subject, the kind of math done by mathematicians, rather than the applied subjects taught in secondary school and the first two years of college. Sometimes a little theory is covered in those courses, but usually not much. Some high schools teach significant theory in geometry, but that comes before most students have developed much mathematical maturity, and I'm afraid the enjoyment and significance of theory are lost on most.
The main topics of the book are (1) countably infinite sets of "words", (2) countably infinite sets of numbers, (3) uncountably infinite sets of strings, numbers, functions, and sets, including Cantor's theorem, (4) paradoxes of set theory, including Russell's paradox, and (5) computable functions.
Along the way related topics are touched on, including base numeral systems, representations of rational and irrational numbers, polynomial equations and algebraic numbers, transcendental numbers, the cubic formula, the irrationality of the square root of two and other integers, functions (onto, 1-1), self-descriptive sequences, discrete dynamical systems, including chaotic systems, semantic paradoxes, Euclid’s theorem, the twin-prime conjecture, limits, continuity, the Fibonacci sequence, inductive/recursive definitions, and proofs by induction.
There are about 100 problems with solutions to almost all.
Request for feedback: Most teachers want feedback, and when teaching it is plentiful and immediate. I would like feedback to this book; please send corrections, comments, and questions to [email protected]
5By Conan BFinally I get this ebook, thanks for all these Infinite Sets I can get now!
4By Jerri UMy friends are so mad that they do not know how I have all the high quality ebook which they do not!
3By Morse JInfinite Sets was the best books I ever buy. Infinite Sets did exactly what you said it does.
4By Sybil EI would like to personally thank you for your outstanding books. It's really wonderful.
3By Dewey KI will recommend you to my colleagues. Infinite Sets is the most valuable books we have EVER purchased. I'd be lost without this. I am completely blown away.
3By Yoshi Ahahahahaha
1By Ivett Lwtffff i do not understand this!