Divergence: What to Do Till the Mathematician Comes: Difference between revisions
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==Abstract== | ==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 | 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|divergence till mathematician comes]] | [[Category:Scientific Paper|divergence till mathematician comes]] | ||
Latest revision as of 13:52, 22 July 2026
| Scientific Paper | |
|---|---|
| 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.