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Topic: Almost infinite
Replies: 19   Last Post: Mar 21, 2013 2:40 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Almost infinite
Posted: Mar 17, 2013 5:57 AM
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On 12/11/2012 9:58 PM, David R Tribble wrote:
> We see the phrase "almost infinite" (or "nearly infinite", or "infinite
> for all practical purposes") in much literature for the layman, usually
> to describe a vastly large number of combinations or possibilities from
> a relatively large number of items. For example, all of the possible
> brain states for a human brain (comprising about 3 billion neurons), or
> all possible combinations of a million Lego blocks, etc.
>
> Obviously, these are in actuality just large finite numbers; having an
> infinite number of permutations of a set of objects would require the
> set to be infinite itself, or the number of possible states of each
> element would have to be infinite. Most uses of the term "infinite
> possibilities" or "almost infinite" are, in fact, just large finite
> numbers. All of which are, of course, less than infinity.
>
> But is there some mathematically meaningful definition of "almost
> infinite"? If we say that m is a "nearly infinite" number, where
> m < omega, but with m having some property that in general makes it
> larger than "almost all" finite n?
>
> Personally, I don't think there is such a definition; but then I would
> enjoy being proved wrong.
>
> -drt
>


Is this a joke?


This exact post was made some time ago.

I answered without being sufficiently precise
with a mention of sequences that do not converge
and William Elliot corrected me by demonstrating
a periodic sequence that did not converge nor
become unbounded.






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