
Re: Almost infinite
Posted:
Dec 17, 2012 9:33 PM


On Wednesday, December 12, 2012 11:27:50 AM UTC5, 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.

