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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:
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> > On Tue, 11 Dec 2012, fom wrote:
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> >> On 12/11/2012 9:58 PM, David R Tribble wrote:
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> >
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> >>> We see the phrase "almost infinite" (or "nearly infinite", or
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> >>> "infinite for all practical purposes") in much literature for the
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> >>> layman, usually to describe a vastly large number of combinations or
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> >>> possibilities from a relatively large number of items. For example,
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> >>> all of the possible brain states for a human brain (comprising about 3
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> >>> billion neurons), or all possible combinations of a million Lego
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> >>> blocks, etc.
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> >>>
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> >>> Obviously, these are in actuality just large finite numbers; having an
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> >>> infinite number of permutations of a set of objects would require the
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> >>> set to be infinite itself, or the number of possible states of each
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> >>> element would have to be infinite. Most uses of the term "infinite
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> >>> possibilities" or "almost infinite" are, in fact, just large finite
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> >>> numbers. All of which are, of course, less than infinity.
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> >>>
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> >>> But is there some mathematically meaningful definition of "almost
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> >>> infinite"? If we say that m is a "nearly infinite" number, where m <
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> >>> omega, but with m having some property that in general makes it larger
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> >>> than "almost all" finite n?
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> >>>
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> >>> Personally, I don't think there is such a definition; but then I would
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> >>> enjoy being proved wrong.
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> >>
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> >> When people look at completeness of the real number system, they are
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> >> looking at convergent sequences attaining a bound within some finite
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> >> distance of the origin.
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> >>
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> > ... sequences attaining a bound within
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> > some arbitrary distance of the limit.
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> >
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> >> The construction of the real numbers
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> >> usually involves considering such sequences
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> >> of rational numbers AS the real number.
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> >
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> > ... involves considering equivalence classes of such
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> > sequences of rational numbers as the real numbers.
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> >
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> >> The "opposite" of this would be a divergent
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> >> sequence that is unbounded.
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> >
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> > The opposite of a convergent sequence, by definition,
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> > is a divergence sequence. A divergent sequence can
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> > approach oo, -oo or oscillates or oscillates within a region.
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> >
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> >> The sequence itself never gets to and infinite distance from the origin.
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> >> But, it grows larger than any convergent sequence.
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> >>
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> > The divergent sequence (sin n)_n doesn't grow larger than the convergence
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> > sequence (3 - 1/n)_n.
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> >
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> >> Hopefully, someone may have a better suggestion for you.
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> >
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> > How so? It seems unrelated to his puzzling.
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> >
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>
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> As I was not concerned with making a statement
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> so precise as to be incomprehensible to someone
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> asking a question about naive intuition, I was not
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> making a claim about every sequence that does not
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> converge.
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>
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> You know just enough mathematics to demonstrate
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> the poverty of your personality.
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>
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> As I recall, when we first met, you were
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> unable to recognize a properly negated conditional
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> 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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