In article <503d7653-f1a6-4d24-b9eb-b39b34a78b5e@i6g2000yqj.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 28 Mai, 20:39, Virgil <virg...@nowhere.com> wrote: > > but the laws of logic are derived from thoughts of an ideal > > world and such thoughts are not obtained solely reality, but from > > largely from an unreal vision of the ideal. > > The result is in due shape. > > > > There > > > > > is no model of a complete linear set in reality that makes [*] false > > > and [**] true. But there are many models showing that [*] is true > > > whenever [**] is true. > > > > And many models for which "ExAy P(x,y) ==> AyEx P(x,y)" is false. > > Not linear models. The naturals and the integers, and the set of unit fractions, and a lot of other models. > > > > > Then WM better confine his attentions to areas in which no limiting > > processes are wanted and no infinite sets are wanted, which excludes him > > from all calculus. > > Either Cantor¹s diagonal proof shows that the limit of all omega > indices can be reached by defining b_n =/= a_n for every n.
Or what?
> Then my binary tree proof shows that the limit of all omega levels can > be reached by showing that the number of distinct lines is countable > at every level n.
Such a "proof" is no proof, as it requires assumptions contrary to fact.
Then all reals are countable.
In WM's personal world of MathUnrealism, he may, if he chooses , declare that 2 = 1, but he has no power to declare anything new outside that world without better "proofs" than he has yet been able to create.
> (Only a very confused > mind could consider the possibility that paths of the infinite tree > and decimal expansions of real numbers might represent different > mathematical objects).
The WM must be saying that every path in a complete infinite binary tree "is identical to" the decimal expansion of a real number AND every decimal expansion of a real number "is identical to" a path in such a binary tree.
Nonsense. For one thing, 0.1(0) and 0.0(1), where (x) indicates an infinite sequence of repetitions of x, represent the same real but different paths. > > Or the limit of the paths in the binary tree does not yield all real > numbers.
They can be made to produce reals, but to get a bijection between strings and reals is not anywhere as trivial as WM thinks it is, and there is no single way to do it that is more natural and obvious that anall others
> Then Cantors diagonal proof does not establish complete real number > either, and the proof is void.
Cantor's diagonal proof does not refer to real numbers at all. Suitable modifications of it done later by others also shows that no list of reals can exhaust all reals. But Cantor had already proved that separately before coming up with his diagonal argument. > > > > > > > > > > This had already been recognized by the late Alexander Zenkin, one of > > > the brave scientists who dared to condemn this hypocritical behaviour > > > > Scientists may mess with physics to their hearts content, but as > > scientists, have no business messing with pure mathematics. > > Mathematics is science done by scientists.
That may be the egotist scientist's pint of view, but it is a false view.
> Matheology is what you may > have in mind. And in fact : That has as much to do with science as has > astrology to with astronomy.
What goes on in WM's wee weird world of MathUnrealism is not mathematics, so much as bad engineering. > > > > > So if anyone introduced any "false logic", it would be physicists rather > > than mathematicians. > > I should refrain from calling what you and your ilk do : matheology. > It could be understood by lurkers as if your hobby was based upon > logic.
I have all sorts of hobbies. One of them is revealing the foolishness of egotistists like WM.
