In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 28 Jun., 17:38, Tonico <Tonic...@yahoo.com> wrote: > > On Jun 28, 2:38 pm, Frederick Williams <freddywilli...@btinternet.com> > > wrote: > > > > > So he is too a fool, and a rather big one, just as Kroenecker was wrt > > Cantor, both personally and mathematically and > > > Sorry, did Kronecker die in a mad house? Or was that Cantor?
> Did Kronecker intrigue against Cantor? I do not know of such action?
Those who do not want to see will manage not to see.
> I know of many intrigues that Cantor started against colleagues - > although without success, luckily.
What WM claims are intrigues are no more than disagreements on what mathematics is all about. > > Fro instance: > I never fully agreed with Dedekind's paper. [Cantor to Jourdain, July > 18, 1901] > > In vol. XXII, no. II of the Annalen pag. 249, Klein has his paper > about function strips printed again which I always have considered the > non plus ultra of higher nonsense, although Mr. Klein refers to the > wisdom of Mr. Kronecker. If you have read my essay Grundlagen > attentively, you will find, that I, on pag. 9, 10, 11 and on pag. 19 > and 20, attack and condemn just these opinions of Kronecker in > strongest terms; on pag. 20, in another matter, I make him a > compliment, together with Dedekind however (that will very much annoy > him). [Cantor to Mittag-Leffler, Sept. 9, 1883]
And there are papers by Kronecker even more vociferously opposed to Cantor's mathematics. Such disagreements on techical matters are not the same as personal attacks
> > Instead of complaining and laughing about your own stupidity you > should try to understand the following disproof of uncountability: > > Take a ring of circumference 1. In the first step construct aleph_0 > pairs of endpoints in an arbitrary way. Then let the endpoints slide > in an arbitrary way. They could in principle reach the configuration > of the intervals I_n covering the rationals q_n with length 10^-n. > This is not excluded as a final state - if the I_n can be brought to > existence at all. In mathematics the aleph_0 complementary intervals > will never become uncountably many > singletons during this continuous process.
This only demonstrates WM's foolishness in claiming that a set of intervals whose lengths add up to only 1/9 can cover all but countably many points of an interval of length 1.
if his were the case, one could cover those uncovers countably many points by another set of intervals of cumulative lengths 1/9.
And by simple extensions of WM's claims one can prove that, at least in his WMatheolology, the outer measure of any finite real interval is less that any positive epsilon. > > Or consider the covering of all rationals q_n by intervals I_n of > length sqrt(2)*10^-n. Then the endpoints are irrational - and there is > no number between two intervals, at least not in mathermatics.
Again allowing proof that all finite intervals are of outer measure zero! -- "Ignorance is preferable to error, and he is less remote from the- truth who believes nothing than he who believes what is wrong. Thomas Jefferson