Constructive Mathematics
نویسنده
چکیده
منابع مشابه
On the Lebesgue Measurability of Continuous Functions in Constructive Analysis
The paper opens with a discussion of the distinction between the classical and the constructive notions of "computable function." There then follows a description of the three main varieties of modern constructive mathematics: Bishop's constructive mathematics, the recursive constructive mathematics of the Russian School, and Brouwer's intuitionistic mathematics. The main purpose of the paper i...
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In the early twentieth century, L.E.J. Brouwer pioneered a new philosophy of mathematics, called intuitionism. Intuitionism was revolutionary in many respects but stands out -mathematically speakingfor its challenge of Hilbert’s formalist philosophy of mathematics and rejection of the law of excluded middle from the ‘classical’ logic used in mainstream mathematics. Out of intuitionism grew intu...
متن کاملConstructive Mathematics , in
The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics (BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin...
متن کاملConstructive Mathematics in Theory and Programming Practice
The first part of the paper introduces the varieties of modem con-structive mathematics, concentrating on Bishop's constructive mathematics(BISH). It gives a sketch of both Myhill's axiomatic system for BISH and aconstructive axiomatic development of the real line R. The second part of the pa-per focusses on the relation between constructive mathematics and programming,with ...
متن کاملFive Stages of Accepting Constructive Mathematics
On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced c...
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This paper gives the beginnings of a development of the theory of fixed point theorems within Bishop’s constructive analysis. We begin with a constructive proof of a result, due to Borwein, which characterises when some sets have the contraction mapping property. A review of the constructive content of Brouwer’s fixed point theorem follows, before we turn our attention to Schauder’s generalisat...
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