From f61026119df4700f69eb73e95620bc5928ca0fcb Mon Sep 17 00:00:00 2001
From: User <bnewbold@daemon.robocracy.org>
Date: Tue, 13 Oct 2009 02:52:09 +0000
Subject: Grand rename for gitit transfer

---
 math/numbers | 54 ------------------------------------------------------
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 delete mode 100644 math/numbers

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-========================
-Numbers
-========================
-
-.. note::
-    incomplete
-
-.. note:: 
-    Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
-
-.. contents::
-
-*incommensurable*
-    objects are incommensurable when their ratio isn't rational
-
-Real Numbers
-==================
-The *real numbers* are defined via Dedakind cuts in [rudin]_, or [meserve]_ 
-(1-12).
-
-Complex Numbers
-==================
-The *complex numbers* are constructed as an ordered pair of real numbers.
-
-Algebraic and Transendental Numbers
-===============================================
-*Algebraic numbers* are solutions of polynomials, such as x in
-:latex:`$a_0 x^n + a_1 x^{n-1} + a_2 x^{n-2} + ... a_n = 0$`, where all a are
-real numbers. *Transcendental numbers* are not solutions to any such 
-polynomials.
-
-All real numbers are either algebraic or transcendental. 
-
-Some algebraic numbers aren't real (such as :latex:`$i = \sqrt{-1}$`). They
-can be rational or irrational. All transcendental numbers are irrational;
-some are not real.
-
-Exersize: is the square root of 5 algebraic or transcendental?
-
-e
-========
-:latex:`$e = \lim_{x \rightarrow 0} (1+x)^{\frac{1}{x}}$`
-
-Infinities
-==================
-*aleph-zero* (:latex:`$\aleph_0$`) is the countably infinite set.
-
-Positive integers, integers, and rational numbers are all countably infinite.
-
-It is unproven that the real numbers are *aleph-one* (:latex:`$\aleph_1$`).
-
-.. [rudin] `Principles of Mathematical Analysis (3rd ed)`:title:, by Walter Rudin. McGraw-Hill, 1976
-
-.. [meserve] `Fundamental Concepts of Algebra`:title:, by Bruce Meserve.
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