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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 44 will matter, so let me discuss it briefly. (See any book on abstract algebra for a more detailed and systematic discussion.) First, let me introduce some well-known sets: 0 As explained above, 1N means the set of all nonnegative integers: ]N = {0,1,2,...}. 0 Furthermore, Z means the set of all integers: Z = {. . . , —2, —1, O, 1, 2,. . ..} o Moreover, Q means the set of all rational numbers: Q = {g | a E Z, l? E Z \ {0}}. 0 Furthermore, IR means the set of all real numbers. This contains rational 5 numbers such as —2 and —, but also irrational numbers such as x/E and 3 \/§ 1 + \3/3 and 7T (and various others, many of which cannot even be described in words 21). :- Finally, C means the set of all complex numbers. They will be rarely used in these notes (indeed, most of linear algebra can be done without them, ex- cept for eigenvalue/ eigenvector theory), so you do not actually have to know them in order to read these notes. However, let me give a quick briefing on ...
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