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Home > Art, Film & Photography > One: Identity Element, Identity Function, Unit Interval, Unary Numeral System, 1, Root of Unity, Unit Vector, Identity Matrix, Empty Product
One: Identity Element, Identity Function, Unit Interval, Unary Numeral System, 1, Root of Unity, Unit Vector, Identity Matrix, Empty Product

One: Identity Element, Identity Function, Unit Interval, Unary Numeral System, 1, Root of Unity, Unit Vector, Identity Matrix, Empty Product


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 36. Chapters: Identity element, Identity function, Unit interval, Unary numeral system, 1, Root of unity, Unit vector, Identity matrix, Empty product, Uniqueness quantification, 0.999..., One-dimensional symmetry group, Unit sphere, Unit fraction, Unit circle, Unit disk, 1, Unit hyperbola, Normalizing constant, One-parameter group, One-form, Singleton, Unital algebra, 1 + 1 + 1 + 1 + ..., Unit ring, Unit square, Trivial ring, Matrix of ones, 1/2 + 1/4 + 1/8 + 1/16 + . . ., Unit cube, Unit function. Excerpt: In mathematics, the repeating decimal 0.999... (which may also be written as 0., 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number. Proofs of this equality have been formulated with varying degrees of mathematical rigour, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience. That certain real numbers can be represented by more than one digit string is not limited to the decimal system. The same phenomenon occurs in all integer bases, and mathematicians have also quantified the ways of writing 1 in non-integer bases. Nor is this phenomenon unique to 1: every nonzero, terminating decimal has a twin with trailing 9s, such as 8.32 and 8.31999... The terminating decimal is simpler and is almost always the preferred representation, contributing to a misconception that it is the only representation. The non-terminating form is more convenient for understanding the decimal expansions of certain fractions and, in base three, for the structure of the ternary Cantor set, a simple fractal. The non-unique form must be taken into account in a classic proof of the uncountability of the entire set of real numbers. Even ...


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Product Details
  • ISBN-13: 9781233053872
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Weight: 86 gr
  • ISBN-10: 1233053876
  • Publisher Date: 15 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Identity Element, Identity Function, Unit Interval, Unary Numeral System, 1, Root of Unity, Unit Vector, Identity Matrix, Empty Product
  • Width: 189 mm


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