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?
Isn't computational results what is to be deemed as correct mathematics. 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. 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. Afterall you mathematicians use these results in computational theory don't you?