Divergence: What to Do Till the Mathematician Comes
|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|
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.