constructive mathematicsの例文

• As such constructive mathematics also rejects the law of excluded middle.
• The status of the axiom of choice varies between different varieties of constructive mathematics.
• Flat modules have increased importance in constructive mathematics, where projective modules are less useful.
• For more see constructive mathematics and Intuitionism.
• A second thread in the history of foundations of mathematics involves nonclassical logics and constructive mathematics.
• In 1966 he was invited to speak at the International Congress of Mathematics on constructive mathematics.
• The book was first reviewed by Errett Bishop, noted for his work in constructive mathematics.
• In particular, the real numbers are also studied in reverse mathematics and in constructive mathematics.
• Variations of the fundamental concept are used in different branches of constructive mathematics and logic programming.
• The study of constructive mathematics includes many different programs with various definitions of " constructive ".
• The intuitionistic school did not attract many adherents among working mathematicians, due to difficulties of constructive mathematics.
• Normal algorithms have proved to be a convenient means for the construction of many sections of constructive mathematics.
• In constructive mathematics, a statement may be disproved by giving a counterexample, as in classical mathematics.
• Non-constructive mathematics in these systems is possible by adding operators on continuations such as canonicity and parametricity.
• This idea is appealing from a Bishop and Richman call the " Russian school " of constructive mathematics.
• In the later part of his life Bishop was seen as the leading mathematician in the area of constructive mathematics.
• Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.
• The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.
• In constructive mathematics, Cauchy sequences often must be given with a " modulus of Cauchy convergence " to be useful.
• However, this well-ordering property does not hold in constructive mathematics ( it is equivalent to the principle of excluded middle ).