transfinite number

transfinite number
any of several numbers which are infinite, but which are not equal to each other. They are represented by the Hebrew letter aleph (ℵ, א) with subscripts 0, 1, etc.

At the beginning of Xanadus second decade of development, Nelson was pleased with the projects caretakers. The last time he had come this close to having a working prototype was in 1972, when time ran out on his rented Nova. Now, the inventors brainchild was more mature. Miller and Gregory created an addressing system that used transfinite numbers, an arcane area of calculus they had both studied in college. They called the new addresses "tumblers"; the tumbler system allowed readers to create links to any arbitrary span of bytes, whether or not the author had marked them. With tumblers, Miller and Gregory could give a similar address to every document and fragment of a document in Xanadus sprawling domain of words, pictures, movies, and sounds. The address would not only point the reader to the correct machine, it would also indicate the author of the document, the version of the document, the correct span of bytes, and the links associated with these bytes.

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  • Transfinite number — Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the… …   Wikipedia

  • transfinite number — Math. an infinite cardinal or ordinal number. [1900 05] * * * ▪ mathematics       denotation of the size of an infinite collection of objects. Comparison of certain infinite collections suggests that they have different sizes even though they are …   Universalium

  • transfinite number — Math. an infinite cardinal or ordinal number. [1900 05] …   Useful english dictionary

  • number — The natural numbers are 0, 1, 2, 3… The integers are…–3, –2, –1, 0, 1, 2, 3…The rationals, as their name implies, measure ratios: any number that can be written as a/b, where a and b are integers, and b ? 0 (in other words, values of x that give… …   Philosophy dictionary

  • Transfinite arithmetic — In mathematics, transfinite arithmetic is the generalization of elementary arithmetic to infinite quantities like infinite sets. It was originally invented by the German mathematician Georg Cantor. See also * transfinite number * cardinal… …   Wikipedia

  • transfinite — /trans fuy nuyt/, adj. 1. going beyond or surpassing the finite. n. 2. See transfinite number. [1900 05; TRANS + FINITE] * * * …   Universalium

  • Transfinite induction — is an extension of mathematical induction to well ordered sets, for instance to sets of ordinals or cardinals. Transfinite induction Let P(α) be a property defined for all ordinals α. Suppose that whenever P(β) is true for all β < α, then P(α) is …   Wikipedia

  • transfinite — [transfī′nīt] adj. 1. extending beyond or surpassing the finite 2. Math. designating or of a cardinal or ordinal number that is larger than any positive integer …   English World dictionary

  • Number — For other uses, see Numbers (disambiguation). A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational… …   Wikipedia

  • number game — Introduction       any of various puzzles and games that involve aspects of mathematics.       Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved.… …   Universalium

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