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

 Messages: [ Previous | Next ]
 LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: 2 Questions on Infinity
Posted: Oct 15, 2013 5:43 PM

"Julio Di Egidio" <julio@diegidio.name> wrote in message
news:l3kcmp\$9ac\$1@dont-email.me...
> "netzweltler" <reinhard_fischer@arcor.de> wrote in message

>>
>> 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.

Date Subject Author
10/14/13 netzweltler
10/14/13 Robin Chapman
10/14/13 Richard Tobin
10/14/13 Ben Bacarisse
10/14/13 fom
10/23/13 Shmuel (Seymour J.) Metz
10/23/13 fom
11/4/13 Shmuel (Seymour J.) Metz
10/14/13 Peter Percival
10/14/13 fom
10/14/13 Brian Q. Hutchings
10/15/13 LudovicoVan
10/15/13 LudovicoVan