Re: I Think I Just Broke a Glass into an Infinite Number of Pieces

"mimus" <tinmimus99@[EMAIL PROTECTED]
> wrote in message 
news:WZGdnYk6ysIsorXVnZ2dnUVZ_qHinZ2d@[EMAIL PROTECTED]
> On Mon, 12 May 2008 18:36:20 +1000, Peter Webb wrote:
>
>> "mimus" <tinmimus99@[EMAIL PROTECTED]
> wrote in message
>> news:8uCdnZuH0sBCzIDVnZ2dnUVZ_hKdnZ2d@[EMAIL PROTECTED]
>>
>>> On Sat, 03 May 2008 21:33:59 -0500, Tim Weaver 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.
>>>>>
>>>>> Maybe this is a sign I should mop my kitchen-floor.
>>>>>
>>>>> Will I need an infinite mop?
>>>>
>>>> Yes, if you have a mobius shaped floor.
>>>
>>> Mobius strips are usually finite.
>>>
>>> Just unbounded.
>>
>> Technical note: Mobius strips have a single boundary.
>
> ok fine.
>
> (As soon as I read that, my head tried to encompass an unbounded Moebius
> strip and couldn't do it.)
>

Well ...

Imagine the width of the Mobius strip was infinite. You would then have a 
surface that was unbounded in both directions, finite in one direction and

infinite in the other - sort of like a cylinder, but its not. Nor is it a 
Klein bottle or cross-cap. It can't be embedded in R^3 as it self 
intersects. But it is a reasonable interpretation of an "unbounded Mobius 
strip", whatever its real name is (if it has one).