• Thumbnail for Paul Halmos
    Paul Richard Halmos (Hungarian: Halmos Pál; 3 March 3 1916 – 2 October 2006) was a Hungarian-born American mathematician and probabilist who made fundamental...
    18 KB (1,746 words) - 20:22, 15 November 2024
  • Thumbnail for Tombstone (typography)
    right aligned). It is sometimes called a "Halmos finality symbol" or "halmos" after the mathematician Paul Halmos, who first used it in a mathematical context...
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  • symbol was later called the tombstone, the Halmos symbol, or even a halmos by mathematicians. Often the Halmos symbol is drawn on chalkboard to signal the...
    12 KB (1,262 words) - 01:16, 23 October 2024
  • Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic analogous...
    1 KB (110 words) - 06:02, 10 May 2024
  • the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. Originally published...
    16 KB (2,603 words) - 08:41, 12 October 2024
  • Paul Halmos, and Alain Connes. These criticisms are analyzed below. The evaluation of nonstandard analysis in the literature has varied greatly. Paul...
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  • Thumbnail for John von Neumann
    Glimm, Impagliazzo & Singer (1990), p. 39. Halmos 1958, p. 86. Halmos 1958, p. 87. Pietsch 2007, p. 168. Halmos 1958, p. 88. Dieudonné 2008. Ionescu-Tulcea...
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  • Martians. Individuals named as members of The Martians group include: Paul Erdős Paul Halmos Theodore von Kármán John G. Kemeny John von Neumann George Pólya...
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  • logic. Paul Halmos discovered monadic Boolean algebras while working on polyadic algebras; Halmos (1962) reprints the relevant papers. Halmos and Givant...
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  • the National Bureau of Standards. He completed his Ph.D. in 1954 under Paul Halmos; his thesis was titled Spectral Theory for Operations on Banach Spaces...
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  • careful analysis of the data acquired in this pursuit." As expressed by Paul Halmos: "Mathematics is not a deductive science—that's a cliché. When you try...
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  • Thumbnail for Paul (given name)
    (1914–1980), American labor leader Paul Halley (born 1952), English keyboardist, vocalist and composer Paul Halmos (1916–2006), Hungarian-born American...
    96 KB (11,331 words) - 19:18, 18 November 2024
  • Grimmett (born 1950) Alice Guionnet (born 1969) Ian Hacking (1936–2023) Paul Halmos (1916–2006) Joseph Halpern (born 1953) David Heath (c.1943–2011) Wassily...
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  • existence (via the axiom of choice), not an explicit example. According to Paul Halmos, a subset of a locally compact Hausdorff topological space is called...
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  • prize, endowed in 2005 by Paul and Virginia Halmos, is named in honor of AMS President Joseph L. Doob, who was Paul Halmos's doctoral advisor in the department...
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  • Thumbnail for Nonstandard analysis
    Journal of Mathematics. Some of the ideas used in Halmos' proof reappeared many years later in Halmos' own work on quasi-triangular operators. Other results...
    31 KB (3,972 words) - 04:00, 25 September 2024
  • Cardinals (1974). ISBN 0 444 10535 2. Halmos 1974, p. 9. Halmos 1974, p. 10. Jech 2002, p. 4. Halmos 1974, Chapter 2. Halmos 1974, See discussion around Russell's...
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  • Mathematics from the University of Michigan; his Ph.D. thesis advisor was Paul Halmos. His thesis, "On lattices of invariant subspaces" concerns operators...
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  • support of the Halmos family for the awards. Halmos himself received the award in 1971 and 1977. The recipients of the Paul R. Halmos – Lester R. Ford...
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  • Surprised?, Fernando Q. Gouvêa, American Mathematical Monthly, March 2011. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted...
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  • Axiom des Unendlichen p. 266f. "Metamath Proof Explorer". Metamath. Paul Halmos (1960) Naive Set Theory. Princeton, NJ: D. Van Nostrand Company. Reprinted...
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  • 2024-06-10. Burgess, John, 2005. Fixing Frege. Princeton Univ. Press. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted...
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  • Kelley's 1955 book General Topology. Its invention is often credited to Paul Halmos, who wrote "I invented 'iff,' for 'if and only if'—but I could never...
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  • Thumbnail for Logarithm
    mathematicians disapprove of this notation. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation", which he said...
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  • Thumbnail for Natural number
    mathematicians such as George A. Wentworth, Bertrand Russell, Nicolas Bourbaki, Paul Halmos, Stephen Cole Kleene, and John Horton Conway have preferred to include...
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  • will need an adjustment instead. Extensionality for a general overview. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted...
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  • Thumbnail for Mathematical proof
    a rectangle, such as □ or ∎, known as a "tombstone" or "halmos" after its eponym Paul Halmos. Often, "which was to be shown" is verbally stated when writing...
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  • unconfirmed moons 2 (algebra), the two-element Boolean algebra, for which Paul Halmos introduced the bolded "2" notation ②, the Stenhaus-Moser number also...
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  • Thumbnail for Marshall H. Stone
    While chairman, Stone hired several notable mathematicians including Paul Halmos, André Weil, Saunders Mac Lane, Antoni Zygmund, and Shiing-Shen Chern...
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  • in 1933, formalized it using the Radon–Nikodym theorem. In works of Paul Halmos and Joseph L. Doob from 1953, conditional expectation was generalized...
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