> Jim Langston wrote:
>

>> Tim Weaver wrote:
>>

>>> mimus wrote:
>>>

>>>> 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.
>>>>
>>>> Neener.

>>>
>>> By the time you get back to where you started, it's dirty again.
>>> Infinite mopping. Of course, you could try to find a mop that mops
>>> an infinite area in one go.

>>
>> Yes, but then you'd need an infinite amount of water to mop the infinite
>> amount of floor, and since an infinite amount of water would take up an
>> infinite amount of space there'd be no room for the floor to begin with.

>
> Consider a cylindrical (in a broad sense) bucket the boundary of the
> base of which is a Koch (snowflake) curve. Since the curve has infinite
> length but encloses a finite area, the bucket has an infinite surface
> area but encloses a finite area. So, roll up your infinite area kitchen
> floor to form such a bucket and you can cover it with a finite amount of
> water simply by filling the bucket.