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  2. Mathematical logic - Wikipedia

    en.wikipedia.org/wiki/Mathematical_logic

    A second thread in the history of foundations of mathematics involves nonclassical logics and constructive mathematics. The study of constructive mathematics includes many different programs with various definitions of constructive. At the most accommodating end, proofs in ZF set theory that do not use the axiom of choice are called ...

  3. Constructivism (philosophy of mathematics) - Wikipedia

    en.wikipedia.org/wiki/Constructivism_(philosophy...

    In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that

  4. Knowledge building - Wikipedia

    en.wikipedia.org/wiki/Knowledge_building

    Students contribute to the collective building of knowledge. · Constructive use of authoritative sources. All participants, including teachers, stand the call as a natural approach to support their understanding. · The conversation of building knowledge. Students are engaged in conversation to share and improve the advancement of knowledge in ...

  5. Constructivism (philosophy of education) - Wikipedia

    en.wikipedia.org/wiki/Constructivism_(philosophy...

    Constructivism in education is rooted in epistemology, a theory of knowledge concerned with the logical categories of knowledge and its justification. [3] It acknowledges that learners bring prior knowledge and experiences shaped by their social and cultural environment and that learning is a process of students "constructing" knowledge based on their experiences.

  6. Constructivist teaching methods - Wikipedia

    en.wikipedia.org/wiki/Constructivist_teaching...

    This is different from a traditional classroom where students primarily work alone, learning through repetition and lecture. Activities encouraged in constructivist classrooms include: Experimentation: Students individually perform an experiment and then come together as a class to discuss the results.

  7. Constructive analysis - Wikipedia

    en.wikipedia.org/wiki/Constructive_analysis

    From this perspective, the full IVT fails in constructive analysis simply because constructive analysis does not accept classical logic. Conversely, one may argue that the true meaning of IVT, even in classical mathematics, is the constructive version involving the locally non-zero condition, with the full IVT following by "pure logic ...

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