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 diff --git a/math/numbers.page b/math/numbers.pagenew file mode 100644index 0000000..541d174--- /dev/null+++ b/math/numbers.page@@ -0,0 +1,54 @@+========================+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.