WebWe study Lawvere's fixed-point theorem in synthetic computability, which is higher-order intuitionistic logic augmented with the Axiom of Countable Choice, Markov's principle, and the Enumeration axiom, which states that there are countably many countable subsets of N N.
nLab
Every lambda expression has a fixed point, and a fixed-point combinator is a "function" which takes as input a lambda expression and produces as output a fixed point of that expression. An important fixed-point combinator is the Y combinator used to give recursive definitions. Meer weergeven In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Some authors … Meer weergeven The Knaster–Tarski theorem states that any order-preserving function on a complete lattice has a fixed point, and indeed a smallest fixed point. See also The … Meer weergeven • Trace formula Meer weergeven • Fixed Point Method Meer weergeven The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. By contrast, the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that … Meer weergeven • Atiyah–Bott fixed-point theorem • Banach fixed-point theorem • Bekić's theorem • Borel fixed-point theorem Meer weergeven 1. ^ Brown, R. F., ed. (1988). Fixed Point Theory and Its Applications. American Mathematical Society. ISBN 0-8218-5080-6. 2. ^ Dugundji, James; Granas, Andrzej (2003). Fixed Point Theory. Springer-Verlag. ISBN 0-387-00173-5. Meer weergeven WebLawvere's fixed-point theorem formalized in Coq with ConCaT Raw LawvereFixedPointTheorem.v (* Lawvere's fixed point theorem. References: F. W. … internet archive get the picture
Cantor
Web301 Moved Permanently. nginx/1.20.1 WebThis question is directly followed by Brouwer's fixed point theorem, which states that any continuous function mapping a compact convex set into itself has fixed point. To show an elementary method, assume there's no fixed point, then f ( x) > x or f ( x) < x for x ∈ [ a, b] since f is continuous. It follows that ( f ( a) − a) ( f ( b) − b) > 0. Web9 jun. 2024 · Russell's Paradox using Lawvere's Fixed Point Theorem 2,016 views Jun 9, 2024 We use Lawvere's Fixed Point Theorem from the video on Cantor's Theorem to prove in a model … new chapter studio