peteolcott

2018-08-20 17:51:56 UTC

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PermalinkWe're not saying the sets in the partition are spherical. Their union is a ball, and the union of their images under a bunch of rotational isometries is two balls. The pieces are made using the axiom of Choice, they are not Boreland sets.

Ah so so are trying to get away with fudging the meaning of the words.If by ball you mean a physically existing object then we are not dealing

with points we are dealing with atoms. If you take away all of the atoms

and divide them into two balls of the same size and shape they now have

half as much mass.

Talking about points on a physically exiting ball is incongruous thus

incoherent. It is either atoms of a ball or points on a sphere. Either

way Banach–Tarski is simply a silly mistake.

Copyright 2018 Pete Olcott

assertion that it is rubbish to have any basis what-so-ever.

First stated in 1924, the Banach-Tarski paradox states that it is

possible to decompose a ball into six pieces which can be reassembled

by rigid motions to form two balls of the same size as the original.

The number of pieces was subsequently reduced to five by Robinson

(1947), although the pieces are extremely complicated.

I contend that it is impossible to decompose any sphere into any

subsets and recompose two identical spheres from these same points.

My proof of that is that when these points are georeferenced

(to eliminate the possibility of inadvertently using the same

points twice) it is self-evident that no method for achieving

the desired end-result can possibly exist.

On the other hand, not having these points georeferenced would

allow the possibility of using the same points twice to go

undetected.

Copyright 2018 Pete Olcott