Difference between revisions of "Divergence: What to Do Till the Mathematician Comes"
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− | It is argued that definitions may be chosen a posteriori to reflect mathematical existence?the opposite of the usual approach by which definitions are chosen a priori and used to prove existence. This inverted view is applied to the question of ?divergence.? It is shown that a definition employing approximations to process remainders known as ?terminal summation? allows ?values? of divergent series to exist.[[Category:Scientific Paper]] | + | It is argued that definitions may be chosen a posteriori to reflect mathematical existence?the opposite of the usual approach by which definitions are chosen a priori and used to prove existence. This inverted view is applied to the question of ?divergence.? It is shown that a definition employing approximations to process remainders known as ?terminal summation? allows ?values? of divergent series to exist. |
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+ | [[Category:Scientific Paper|divergence till mathematician comes]] |
Latest revision as of 10:16, 1 January 2017
Scientific Paper | |
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Title | Divergence: What to Do Till the Mathematician Comes |
Author(s) | Thomas E Phipps |
Keywords | divergence, divergent series, mathematics, definitions, convergence, infinite series, summability, terminal summation, Brown's function, Brown's series, Euler |
Published | 2001 |
Journal | Physics Essays |
Volume | 14 |
Number | 4 |
Pages | 341-353 |
Abstract
It is argued that definitions may be chosen a posteriori to reflect mathematical existence?the opposite of the usual approach by which definitions are chosen a priori and used to prove existence. This inverted view is applied to the question of ?divergence.? It is shown that a definition employing approximations to process remainders known as ?terminal summation? allows ?values? of divergent series to exist.