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

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Porky Pig Jr

Posts: 1,535
Registered: 12/6/04
Re: Almost infinite
Posted: Dec 17, 2012 9:33 PM
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On Wednesday, December 12, 2012 11:27:50 AM UTC-5, fom wrote:
> On 12/12/2012 2:16 AM, William Elliot wrote:
>

> > On Tue, 11 Dec 2012, fom wrote:
>
> >> 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.
>
> >>
>
> >> When people look at completeness of the real number system, they are
>
> >> looking at convergent sequences attaining a bound within some finite
>
> >> distance of the origin.
>
> >>
>
> > ... sequences attaining a bound within
>
> > some arbitrary distance of the limit.
>
> >
>
> >> The construction of the real numbers
>
> >> usually involves considering such sequences
>
> >> of rational numbers AS the real number.
>
> >
>
> > ... involves considering equivalence classes of such
>
> > sequences of rational numbers as the real numbers.
>
> >
>
> >> The "opposite" of this would be a divergent
>
> >> sequence that is unbounded.
>
> >
>
> > The opposite of a convergent sequence, by definition,
>
> > is a divergence sequence. A divergent sequence can
>
> > approach oo, -oo or oscillates or oscillates within a region.
>
> >
>
> >> The sequence itself never gets to and infinite distance from the origin.
>
> >> But, it grows larger than any convergent sequence.
>
> >>
>
> > The divergent sequence (sin n)_n doesn't grow larger than the convergence
>
> > sequence (3 - 1/n)_n.
>
> >
>
> >> Hopefully, someone may have a better suggestion for you.
>
> >
>
> > How so? It seems unrelated to his puzzling.
>
> >
>
>
>
> As I was not concerned with making a statement
>
> so precise as to be incomprehensible to someone
>
> asking a question about naive intuition, I was not
>
> making a claim about every sequence that does not
>
> converge.
>
>
>
> You know just enough mathematics to demonstrate
>
> the poverty of your personality.
>
>
>
> As I recall, when we first met, you were
>
> unable to recognize a properly negated conditional
>
> in a proof.


Putting personality issues aside, your original posting was indeed a 100% nonsense. You know just enough maths to demonstrate being clueless.



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