LudovicoVan
Posts:
4,111
From:
London
Registered:
2/8/08
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Re: 2 Questions on Infinity
Posted:
Oct 15, 2013 5:43 PM
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"Julio Di Egidio" <julio@diegidio.name> wrote in message
news:l3kcmp$9ac$1@dont-email.me...
> "netzweltler" <reinhard_fischer@arcor.de> wrote in message
> news:c05379ba-fe0a-4647-93c6-b19116cd18f5@googlegroups.com...
>>
>> If I am mixing 9 liters of red paint and 1 liter of green paint, the
>> mixture
>> ratio is 9:1. If I am mixing 99 liters of red paint and 1 liter of green
>> paint,
>> the percentage of red paint is 99%. If I am not stopping increasing the
>> percentage of red paint, the percentage of red paint is 99.999?% (even if
>> this
>> means that the whole infinite universe is filled with red paint). But a
>> universe
>> filled with red paint and 1 liter of green paint is different to a
>> universe
>> solely filled with red paint, and no green paint in it. How do we point
>> out this
>> difference using standard decimal notation?
>
> Standardly, we cannot make that difference: we just take the limit of the
> ratio and that is 1/(oo+1)=0, i.e. the ratio tends to 0.
Sorry, not the ratio in your example...
Julio
> For non-standard approaches, along with the references fom has already
> provided, I'll mention the surreal numbers:
> <http://en.wikipedia.org/wiki/Surreal_number>
>
>> If the atoms of this 1 liter of green paint are evenly spread within this
>> infinite universe of red paint, what is the distance between these atoms?
>
> It depends on how the particles of paint are spread exactly: if from a
> single point and at a finite initial velocity, then they will never span
> more than a finite volume (at any finite time). But if they are spread by
> some supernatural action (a supertask), they could even be evenly
> distributed instantaneously and at rest in the infinite universe of
> otherwise red paint. But, again, the standard finitary framework would
> not be able to express any of this in detail.
>
>> If the distance between these atoms is finite and the number of atoms is
>> finite, does it mean, that the space the green atoms are evenly spread in
>> is finite?
>
> Yes, logically.
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