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JimT wrote:
> though I suppose you need to be as old as me to talk about c rather than Aleph_1
The cardinallity of the continuum is equal to Beth-one, which is equal
to Aleph-one if and only if the continuum hypothesis holds. And the
continuum hypothesis is independent of the axioms of ZFC, so...
>> (Then again, one presumes that the gravitational field generated by a
>> countably infinite quantity of green bottles would somewhat exceed the
>> Earth's own gravitation. Although, since it fills a transfinite volume
>> as well... hmm, interesting.)
>>
> If the wall was on earth, the bottles would have to decrease in size, and hence
> mass, in order to fit on it, and no, I haven't decided what to do when the
> volume of a bottle is less than that of a hydrogen atom.
I wonder - is the volume of the universe infinite? (The volume of the
*obvservable* universe clearly isn't.)
For that matter, shouldn't a countable infinity of masses generate
enough gravity to collapse into a singularity?
> I think it is:
>
> 99 bottles of nitro-glycerine ...
>
> nitro being liquid and very susceptible to small shocks. I believe TNT is solid
> and stable unless detonated by explosion.
Apparently so. I was under the impression that they're both equally
unstable, but apparently not.
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