:There are extremely few " natural " mathematical statements that can be stated in second order arithmetic but are not provable in second order arithmetic.
32.
A non-mathematical statement of this law is, " the greatest growth occurs when the greatest number of mistakes are made consistent with survival ".
33.
G�del numbers, and similar numbers used to represent bit-strings in algorithmic information theory, are very large, even for mathematical statements of reasonable length.
34.
In a paper from 2007, Anton Kapustin and Edward Witten suggested that the geometric Langlands correspondence can be viewed as a mathematical statement of Montonen Olive duality.
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The Entscheidungsproblem, proposed by David Hilbert, asked whether there is an effective procedure to determine which mathematical statements ( coded as natural numbers ) are true.
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He put forward a strong empirical position, arguing that all knowledge must either come from observations of the world or be necessarily true, like mathematical statements.
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As the modern foundation of mathematics, is it possible to prove all provable mathematical statements from talk ) 08 : 18, 29 January 2011 ( UTC)
38.
Questions of this kind give rise to a following problem : determine the degree of realizability of the conclusions of mathematical statements in the case of approximate validity of conditions.
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A scientific law is a concise verbal or mathematical statement of a relation which expresses a fundamental principle of some theory, such as Newton's law of universal gravitation.
40.
For the mathematical statement it is perfectly acceptable to omit the conjunction, but if you prefer to include it then I think " or " sounds more logical ."
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