| Re: I Think I Just Broke a Glass into an Infinite Number of Pieces |
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Date: May 20, 2008 05:13
mimus wrote:
>
> On Mon, 19 May 2008 09:54:14 +0100, Frederick Williams wrote:
>
>> mimus wrote:
>>
>>> At least, I swept up at least twice as much glass as could possibly have
>>> been in the original.
>>>
>>> And that's only possible if you do an infinite decomposition of the
>>> object, as exemplified by the Tarski-Banach ball.
>>
>> Not infinite, five pieces suffice. At least it's five in three
>> dimensional space, in one or two dimensions one needs aleph_0 many
>> pieces.
>
> I haven't seen or even heard of any-a these five-piece multiplicative
> reassemblies in 3-space, so I'm getting whiffs of weasel from somewhere.
Raphael M. Robinson proved the result I referred to.
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