• Thumbnail for Paul Halmos
    Paul Richard Halmos (Hungarian: Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician and statistician who made fundamental...
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  • 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...
    14 KB (1,528 words) - 21:14, 9 February 2024
  • Paul Halmos, and Alain Connes. These criticisms are analyzed below. The evaluation of nonstandard analysis in the literature has varied greatly. Paul...
    28 KB (3,520 words) - 22:58, 18 August 2023
  • Gehring, Frederick W., eds. (1991), Paul Halmos: celebrating 50 years of mathematics, Springer-Verlag, Interview of Halmos with Donald J. Albers, p. 16, ISBN 0-387-97509-8...
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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...
    204 KB (23,289 words) - 22:55, 20 April 2024
  • 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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  • Thumbnail for Paul (given name)
    composer Paul Halmos (1916–2006), Hungarian-born American mathematician and statistician Paul Hamm (born 1982), American retired artistic gymnast Paul A Hampton...
    91 KB (10,667 words) - 03:00, 29 April 2024
  • Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic analogous...
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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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  • Apprenticeship of a Mathematician, Springer, p. 114, ISBN 9783764326500. Halmos, Paul (1950). Measure Theory. New York: Van Nostrand. pp. vi. The symbol ∎...
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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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  • 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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  • 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...
    98 KB (11,493 words) - 14:44, 29 April 2024
  • Thumbnail for Squaring the circle
    grand problem no longer unsolved: the circle squared beyond refutation." Paul Halmos referred to the book as a "classic crank book." The problem of squaring...
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  • Thumbnail for Number
    Mathematical Structures, Harcourt Brace Javanovich, 1989, ISBN 0-15-543468-3. Paul Halmos, Naive Set Theory, Springer, 1974, ISBN 0-387-90092-6. Morris Kline,...
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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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  • 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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  • 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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  • vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158 Paul Halmos, "What Does the Spectral Theorem Say?", American Mathematical Monthly...
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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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  • 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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  • Thumbnail for Birthday problem
    outputs are many more. The argument below is adapted from an argument of Paul Halmos. As stated above, the probability that no two birthdays coincide is 1...
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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...
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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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  • 1945) 2006 – Helen Chenoweth-Hage, American politician (b. 1938) 2006 – Paul Halmos, Hungarian-American mathematician (b. 1916) 2007 – Tex Coulter, American...
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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 Theorem
    tombstone marks, such as "□" or "∎", meaning "end of proof", introduced by Paul Halmos following their use in magazines to mark the end of an article. The exact...
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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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  • Russell Autobiography 1967 Freeman Dyson Disturbing the Universe 1979 Paul Halmos I Want to be a Mathematician: An Automathography 1985 Stanislaw Ulam...
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