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1. de.wikipedia.org › wiki › Bedingter_ErwartungswertBedingter Erwartungswert – Wikipedia

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   Vor 6 Tagen · In Arbeiten von Paul Halmos 1950 und Joseph L. Doob 1953 wurden bedingte Erwartungen auf die heute übliche Form von Teil-σ-Algebren auf abstrakten Räumen übertragen.

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3. chalkdustmagazine.com › regulars › big-argumentThe big argument: What’s the best way to end a proof?

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   20. Mai 2024 · Paul Halmos introduced the $\square$ notation for the end of proofs, inspired by end marks in (non-maths) magazines, in the 1950s—and lots of people still call it the ‘halmos’. Honestly, I’d be on board with anything he has to say about writing and typesetting maths.

4. booksandnotes.substack.com › p › paul-halmos-naive-set-theory-8b4Paul Halmos - Naive Set Theory - by Manuel del Rio

   booksandnotes.substack.com › p › paul-halmos-naive-set-theory-8b4

   4. Juni 2024 · SECTION 9. Exercise: formulate and prove a generalized version of the commutative law. First step is trying to get a grasp of the commutative law for unions, and seeing what shape it takes when it generalizes. So the most basic case is for two sets, A and B, where we'd say the commutative law is A∪B = B ∪ A.

5. epsilonjourney.wordpress.com › 2024/05/23 › initial-pointInitial Point – Epsilon

   epsilonjourney.wordpress.com › 2024/05/23 › initial-point

   23. Mai 2024 · So over this period of two months, I’m going to try to continue reading “Naive Set Theory” by Paul Halmos and maybe a book on proof writing. Linear algebra is one branch which interests me, I plan on trying that too, just a little bit of the top. So yeah nothing too complicated, step by step, and we’ll see where it goes.

6. en.wikipedia.org › wiki › First-order_logicFirst-order logic - Wikipedia

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   Vor 2 Tagen · First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics. Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic.

7. en.wikipedia.org › wiki › Type_theoryType theory - Wikipedia

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   6. Juni 2024 · [a] Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: Typed λ-calculus of Alonzo Church. Intuitionistic type theory of Per Martin-Löf.

8. en.wikipedia.org › wiki › Dual_spaceDual space - Wikipedia

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   Vor 17 Stunden · The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space . When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the continuous dual space .