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Informal mathematics information


Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and is the subject of modern ethno-cultural studies of mathematics. The philosopher Imre Lakatos in his Proofs and Refutations aimed to sharpen the formulation of informal mathematics, by reconstructing its role in nineteenth century mathematical debates and concept formation, opposing the predominant assumptions of mathematical formalism.[1] Informality may not discern between statements given by inductive reasoning (as in approximations which are deemed "correct" merely because they are useful), and statements derived by deductive reasoning.

  1. ^ Imre Lakatos, Proofs and Refutations (1976), especially the Introduction.

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usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully...

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many applications to other areas of mathematics as well as the ordinary mode of reasoning of informal mathematics in calculus and applications to physics...

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foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language...

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explains that his purpose is to challenge formalism in mathematics, and to show that informal mathematics grows by a logic of "proofs and refutations". The...

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part of the culture of mathematics, rather than of the subject. Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous...

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containing informal fallacies may be formally valid, but still fallacious. A special case is a mathematical fallacy, an intentionally invalid mathematical proof...

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read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode...

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mass, and c is the speed of light. Use of mathematical jargon that consists of phrases that are used for informal explanations or shorthands. For example...

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books. Concrete Mathematics has an informal and often humorous style. The authors reject what they see as the dry style of most mathematics textbooks. The...

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establish was that no theorem of informal mathematics is final or perfect. This means that, in non-axiomatic mathematics, we should not think that a theorem...

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became easier to reconcile with classical mathematics. Philosophy portal Mathematics portal Argument Informal logic Knowledge representation and reasoning...

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