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  2. Introductio in analysin infinitorum - Wikipedia

    en.wikipedia.org/wiki/Introductio_in_analysin...

    Introductio in analysin infinitorum. Introductio in analysin infinitorum (Latin: [1] Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis. Written in Latin and published in 1748, the Introductio contains 18 chapters in the first part and 22 chapters in the second.

  3. Aleph number - Wikipedia

    en.wikipedia.org/wiki/Aleph_number

    The definition of ℵ 1 implies (in ZF, Zermelo–Fraenkel set theory without the axiom of choice) that no cardinal number is between ℵ 0 and ℵ 1. If the axiom of choice is used, it can be further proved that the class of cardinal numbers is totally ordered, and thus ℵ 1 is the second-smallest infinite

  4. John Saxon (educator) - Wikipedia

    en.wikipedia.org/wiki/John_Saxon_(educator)

    After his first book was published, Saxon published more books: Algebra 1 1/2, Algebra 1/2 and Geometry, Trigonometry and Algebra 3. (He later renamed his book Algebra 1 1/2 simply Algebra 2). His reasoning for titling his second textbook Algebra 1 1/2 is that a good part of the book was a review of Algebra 1 topics.

  5. Von Neumann algebra - Wikipedia

    en.wikipedia.org/wiki/Von_Neumann_algebra

    An example of a type II 1 factor is the von Neumann group algebra of a countable infinite discrete group such that every non-trivial conjugacy class is infinite. McDuff (1969) found an uncountable family of such groups with non-isomorphic von Neumann group algebras, thus showing the existence of uncountably many different separable type II 1 ...

  6. Total order - Wikipedia

    en.wikipedia.org/wiki/Total_order

    If X is any set and f an injective function from X to a totally ordered set then f induces a total ordering on X by setting x 1 ≤ x 2 if and only if f(x 1) ≤ f(x 2). The lexicographical order on the Cartesian product of a family of totally ordered sets, indexed by a well ordered set, is itself a total order.

  7. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

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