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Topic: 2 Questions on Infinity
Replies: 12   Last Post: Nov 4, 2013 8:45 AM

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LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
Re: 2 Questions on Infinity
Posted: Oct 15, 2013 5:39 PM
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"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. 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.

Julio





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