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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Nonstandard Analysis and Vector Lattices (Paperback, Softcover reprint of the original 1st ed. 2000)
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Nonstandard Analysis and Vector Lattices (Paperback, Softcover reprint of the original 1st ed. 2000)
Series: Mathematics and Its Applications, 525
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Nonstandard methods of analysis consist generally in comparative
study of two interpretations of a mathematical claim or
construction given as a formal symbolic expression by means of two
different set-theoretic models: one, a "standard" model and the
other, a "nonstandard" model. The second half of the twentieth
century is a period of significant progress in these methods and
their rapid development in a few directions. The first of the
latter appears often under the name coined by its inventor, A.
Robinson. This memorable but slightly presumptuous and defiant
term, non standard analysis, often swaps places with the term
Robinsonian or classical non standard analysis. The characteristic
feature of Robinsonian analysis is a frequent usage of many
controversial concepts appealing to the actual infinitely small and
infinitely large quantities that have resided happily in natural
sciences from ancient times but were strictly forbidden in modern
mathematics for many decades. The present-day achievements revive
the forgotten term infinitesimal analysis which reminds us
expressively of the heroic bygones of Calculus. Infinitesimal
analysis expands rapidly, bringing about radical reconsideration of
the general conceptual system of mathematics. The principal reasons
for this progress are twofold. Firstly, infinitesimal analysis
provides us with a novel under standing for the method of
indivisibles rooted deeply in the mathematical classics."
General
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