Standard Analysis

Some articles on standard analysis, analysis, standard:

Synthetic Differential Geometry - Further Reading
... notation Integral symbol Criticism of non-standard analysis The Analyst The Method of Mechanical Theorems Cavalieri's principle Related branches Non-standar ...
Criticism Of Non-standard Analysis - Bishop's Criticism
... Bishop, classical mathematics, which includes Robinson's approach to nonstandard analysis, was non-constructive and therefore deficient in numerical meaning (Feferman 2000) ... Bishop was particularly concerned about the use of non-standard analysis in teaching as he discussed in his essay "Crisis in mathematics" (Bishop 1975) ... A more recent attempt at mathematics by formal finesse is non-standard analysis ...
Invariant Subspace Problem - Known Special Cases
... Bernstein Robinson (1966) proved using non-standard analysis that if the operator T on a Hilbert space is polynomially compact (in other words P(T) is compact for some ... Halmos (1966), after having seen Robinson's preprint, eliminated the non-standard analysis from it and provided a shorter proof in the same issue of the same journal ...
Criticism Of Non-standard Analysis
... Non-standard analysis and its offshoot, non-standard calculus, have been criticized by several authors ... The evaluation of non-standard analysis in the literature has varied greatly ... to the logical status of the results proved using non-standard analysis ...
Criticism Of Non-standard Analysis - Halmos' Remarks
... They presented their result in the metamathematical language called non-standard analysis, but, as it was realized very soon, that was a matter of personal preference, not necessity." Halmos writes in (Hal. 204) The Bernstein–Robinson proof uses non-standard models of higher order predicate languages, and when sent me his reprint I really had to sweat to pinpoint and translate its mathematical ... While commenting on the "role of non-standard analysis in mathematics", Halmos writes (p ...

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