In article <email@example.com>, JT <firstname.lastname@example.org> 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. --