ultrafinitism


ultrafinitism
A form of finitism that is even more extreme in that it denies those constructs whose construction cannot be physically performed (such as a number that no human could have time to calculate).

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  • Ultrafinitism — In the philosophy of mathematics, ultrafinitism, or ultraintuitionism, is a form of finitism.Ultrafinitists deny the existence of the infinite set N of natural numbers, on the grounds that it can never be completed.In addition, ultrafinitists are …   Wikipedia

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  • Peano axioms — In mathematical logic, the Peano axioms, also known as the Dedekind Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used… …   Wikipedia

  • Philosophy of mathematics — The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of …   Wikipedia

  • Finitism — In the philosophy of mathematics, finitism is an extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps. In her book Philosophy of Set… …   Wikipedia

  • Classical mathematics — In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory.[1] It stands in contrast to other types of mathematics such as constructive …   Wikipedia

  • List of mathematics articles (U) — NOTOC U U duality U quadratic distribution U statistic UCT Mathematics Competition Ugly duckling theorem Ulam numbers Ulam spiral Ultraconnected space Ultrafilter Ultrafinitism Ultrahyperbolic wave equation Ultralimit Ultrametric space… …   Wikipedia

  • Alexander Esenin-Volpin — Alexander Sergeyevich Esenin Volpin ( ru. Александр Сергеевич Есенин Вольпин)is a prominent Russian American poet and mathematician. Born on May 12 1924 in the former Soviet Union, he was a notable dissident, political prisoner, poet, and… …   Wikipedia

  • mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …   Universalium

  • ultrafinitist — noun A proponent of ultrafinitism …   Wiktionary


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