Re: infinity

Virgil said:
> In article <MPG.1d73f4054e8d5f9298a127@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
> > > In article <MPG.1d6e8fcfa148da7898a105@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > Virgil said:
> > >
> > >
> > > > > I want TO to call different things by different names, which is
> > > > > a minimal standard of good mathematics as it is a minimal
> > > > > standard for any attempt to be clear and unambiguous. TO's
> > > > > failure to do so leaves one suspecting that his intent is to be
> > > > > ambiguous and unclear.
> > >
> > > > Oh bull. The same symbols and words are used in different
> > > > contexts within math,
> > >
> > > But what I am objecting to is TO using the same word with different
> > > meanings in the same context, often within the same sentence.
> > >
> > >
> > > > and math uses words that have colloquial meanings for specific
> > > > things, so reuse of terms is not my invention.
> > >
> > > Multiple useage of a word in a single context seems to be one of
> > > TO's less brilliant inventions.
> > >
> > > > > > >
> > > > > > > To which TO has no response.
> > > > >
> > > > > > I have responded.
> > > > >
> > > > > Only by avoiding the issue. That does not qualify as a response
> > > > > to the issue.
> > > > Bull. log2(N) where N is the number of moments in a minute.
>
> The number of moments in a minute is C, not N.
Perhaps. i have reconsidered my equating of [0,1) and N. But, if we want to
restrict our subdivisions so that they are never smaller than 1/N, then we
should consider the time span to contain N such moments.
> > >
> > > Gobbledegook like undefined and undefinable expressions does not
> > > qualify as a response either. There are many algorithms for
> > > calculating logarithms of positive, but finite, real numbers to any
> > > desired degree of accuracy, so that log2(x) for such a positive
> > > finite real x is legitimate.
>
> > And if that formula holds for all initial segments of N, then it
> > holds for N as well.
>
> A formula that holds for all initial segments of N but not for N is that
> the initial segments all have largest members but N does not. Thus TO's
> claim is WRONG AGAIN!
Huyah Huyah Ommmmm......
> > >
> > > Until TO can provide similar algorithms or other evaluations for
> > > log2(N), he has no right to presume any such thing exists. For
> > > example, is log2(N) the cardinality of some known set?
> > Try the set of powers of two.
>
> The set of powers of two {2^x: x in R} is uncountably infinite, and is
> thus larger than the set of naturals.
The set of powers of two {2^x: x in N} is countably infinite, and is
smaller than the set of naturals. Note that this is a function N->R.

> > >
>

--
Smiles,

Tony
.

Relevant Pages

  • Re: infinity
    ... >> Try the set of powers of two. ... Virgil wrote: ... > The set of powers of two is uncountably infinite, ... > thus larger than the set of naturals. ...
    (sci.math)
  • Re: infinity
    ... > distance between values in some set, provided any such maximum exists, ... but to require that any number "occupy space" is quite another. ... >> We ask how many such segments we can ... there are no more than 10 naturals in any open interval of 10 ...
    (sci.math)
  • Re: Why does everyone do it?
    ... naturals N to the even naturals 2N determines a bijection between N ... is NOT the limit of its initial segments and that's precisely what is ... So if what is bothering you, and others as you wrote, is that "N ...
    (sci.math)
  • Re: infinity
    ... >> distance between values in some set, provided any such maximum exists, ... The RANGE of the set of reciprocals of finite positive naturals does not ... > say the range is finite, since the largest difference cannot be infinite. ... >>> We ask how many such segments we can ...
    (sci.math)
  • Re: Why does everyone do it?
    ... naturals N to the even naturals 2N determines a bijection between N ... is NOT the limit of its initial segments and that's precisely what is ... set is infinite": the set of natural numbers, N, fulfills the latter, ...
    (sci.math)