On 1 Maj, 22:29, Virgil <vir...@ligriv.com> wrote: > In article > <28109973-c022-48f7-8171-23b869023...@e9g2000vbg.googlegroups.com>, > > > > > > > > > > JT <jonas.thornv...@gmail.com> wrote: > > On 1 Maj, 21:06, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <1916610b-4cb5-4101-ac80-008cacefd...@o9g2000vbk.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > It is easy. Look at the sequence > > > > 0.1 > > > > 0.11 > > > > 0.111 > > > > ... > > > > Each term has only natural indices. > > > > The limit 0.111... has not only natural indices, because all natural > > > > indices are in the terms of the sequence. So no index or set of > > > > indices remains to distinguish 0.111... from all terms of the > > > > sequence. > > > > While it is true that no single index or even finite set of indices is > > > enough, the infinite set of all indices, being larger than any FISON, is > > > quite enough to distinguish the limit from any term of the sequence. > > > > Note that outside of Wolkenmuekenheim, such infinite sets as the set of > > > all natural numbers, the set of all integers, the set of all rationals > > > and the set of all reals (the last being uncountable) are quite standard. > > > > If WM wishes to create a world of his own where such standard usages are > > > exiled, he is quite free to do so, but cannot expect the vast majority > > > of mathematicians to follow him into his tiny cramped corrupted world. > > > -- > > > But what if it turned out it is other way that it is the > > mathematicians word that are corrupted, and the rest of the world gain > > benefits from finite expressions so if they follow WMs ideas there > > will be gains in enginneering and computational theory and applied > > mathematics? > > Anyone who follows WM's ideas about what mathematics is and how it > should be done, will end up unable to do any but the most trivial of > mathemtaics. > > > Isn't computational results what is to be deemed as correct > > mathematics. > > Computational results are the sine qua non of sciences and most of > applies mathematics but are of considerably less importance in pure > mathematics that constructions, definitions, proofs and such like. > > > If one method leads to approximations and longer > > computational times, and another leads to finite expressions with > > shorter computational time. Will not the faster, finite, none > > approximated approach in the end be math. > > They will both be applied mathematics. And in applications ease and > accuracy of calulation is of great importance. In pure math, ease of > calculation need not always be of primary importance so long SOME method > of calculation can be shown to give the desired result. > > > I mean there is new > > forumulas every day that make faster and better calculations, aren't > > they better and more refined methods then the slower approximations. > > Such formulas are more the province of computer science and programming > than pure mathematics. > > > After all you mathematicians use these results in computational theory > > don't you? > > Most pure mathematics today does not do much with computation theory, > which is mostly left to computer scientists. > --
But you use the programs they write? At least people in theoretical physics do.