LudovicoVan
Posts:
3,815
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@dontemail.me... > "netzweltler" <reinhard_fischer@arcor.de> wrote in message > news:c05379bafe0a464793c6b19116cd18f5@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 nonstandard 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.

