Infinitesimals in the foundations of Newton's mechanics

Sellés, Manuel A.

doi:10.1016/j.hm.2005.04.002

Cited by 6 publications

(3 citation statements)

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“…Corollary .16. Therefore, I draw an conclusion that differential and integral calculus that are continuous calculation of dividend and divisor based on this mixed axim1 and axiom 2 has become not suitable because of existenence of axiom 1 [5].…”

Section: Resultsmentioning

confidence: 98%

“…For instance, 1.3333…… and 1.3333……4 are meaningful and can be aslo found within one system that can be applied for any decimal and integar quantities within it .Taking an example,any decimal quantities can be included within an given system,such as the range of one meter long or Corollary .16. Therefore, I draw an conclusion that differential and integral calculus that are continuous calculation of dividend and divisor based on this mixed axim1 and axiom 2 has become not suitable because of existenence of axiom 1 [5].…”

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confidence: 98%

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A geometry consisting of singularities containing only integers

2021

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It is difficult for us to discriminate the sizes of space and time as finite and infinite. In this article an axiom is defined in which one infinitely small and infinitely great must exist if the sizes of space and time can be compared and it is undividedly 0(zero) point (singularity) for this infinitely small.this axiom have some new characters distinct from current calculus ,such as extension only can be executed in the way of unit superposition in the system, the decimal point is meaningless and there aree only integers to exist in the system, and any given interval is finite quantites and can not be ‘included’ or ‘equal divided’ infinitely and randomly.The geometry space we see are the non-continuum being made of countless 0 points .

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Section: Resultsmentioning

confidence: 98%

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confidence: 98%

A geometry consisting of singularities containing only integers

2021

Preprint

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“…31 The definition of those contributions to be "main" is more or less conventional obeying the specific consideration in the present paper. There exist many enough articles, studies or books discussing different aspects or parts of Newton's heredity, for example : Fox 2016;Kvasz 2016;Palenik 2014;Belkind 2013;Schuster 2011;Darigol 2010;McGuire 2007;Sellés 2006;Iliffe 2004;Reyes 2004;Ramati 2001;Guicciardini 1999;Lamb 1994;Bonsiepen 1993;Graneau, Graneau 1993;Neuser 1993;Snobelen 1998;Garrison 1987;Aoki 1996;Greenberg 1996;Moore 1993;Moretto 1993a;Pater 1993;Petry 1993;Sarlemijn 1993;Steinle 1993;Muraskin 1992;Meli 1991;Whitrow 1989;Hojman, Hojman 1985;Cushing 1982;Cohen 1978;Ramakrishnan 1973;Ferguson 1968;Wisdom 1941;Mordel 1927;Snow, Sugden 1924; mathematics and physics correspondingly and thus even opposed as the organization of modern cognition needs and requires. The latter two contributions, though undoubtedly both belonging to physics, also are not interpreted together, but rather independently of each other, at least until Einstein's general relativity: Indeed, his fundamental principle underlain the foundations of that theory: namely, about the exact equation of gravitational and "inertial" (i....…”

Section: More Reflections About What Gravitation Ismentioning

confidence: 99%