Re: .999... ?= 1

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 09:02:15 +0100

Robin Chapman wrote:

>>I am still touching in the dark. So far I do not know what could be most
>>helpful to me. I just got a new book on signal processing for judgement.
>>Of course, they are sticking in the exclusively complex-valued analysis.
>>I did not find the slightes allusion that time between minus infinity
>>and plus infinity just stems from Heaviside's clever trick and Laurent
>>Schwarz's generalized functions based on IR^înfinity. This omission
>>does not just lead the average reader to the illusion future time is
>>anticipated. More detrimentally, function of the inner ear cannot be
>>understood correctly as long as hoity-toity theorists need weird detours
>>when modelling (British spelling, OK?) it instead of trusting in my
>>pretty simple natural spectrogram.
>>I do not intend to bother mathematicians for nothing.
>
>
> Why are you bothering mathematicians then?

See above. I acknowledge you explained to me why generalized functions
and distributions were introduced. I am still uncertain whether or not
the distributions would also make sense with the restriction to IR+.
Of course, I would not expect such "IR+ distribution" to provide the
derivative of Dirac delta.
To some extent I also ask for clarity how to deal with zero. It is still
my gut feeling that as far as real numbers represent real time,
exclusion of zero like a neutral position between IR+ and IR- does not
make sense. In principle, the whole issue is of no relevance for an
elapsed-time based analysis just within IR+ because in this case there
is no stationary value at zero. Imagine the function of time permanently
moving towards larger elapsed time and getting new values at its origin.
Admittelly, this notion of time is quite uncommon. I merely have to
explain how the analysis in IR+ relates to Heaviside's trick buoying
generations up with seeming symmetry.
Let me add why I do not completely trust in Abraham Robinson's
hyperreals. He reached a lot of improvement. However, he did not abandon
the relations larger equal and smaller. So he cannot release Buridan's
donkey because this would require to accept that integers and other
discrete values are of no special weight (in the sense of distributions)
within a continuum. I see any attempt to completely bridge the gap
between finite and infinite doomed to fail. Why not accepting this and
declare the donkey cheating from the very beginning? It cannot be at a
neutral position if it is expressed in terms of a continuum. A continuum
can be cut through, a number not. Do no longer believe the fairy tail
that integrals and reals are about the same matter.

Eckard

Relevant Pages

  • Re: Probability of picking a positive rational number at random
    ... all uniform distributions over all well-orderings of distributions ... requiring arbitrary well-orderings followed by random distributions ... bijection to the unit interval of reals, ... ordinals being a non-measurable set, ...
    (sci.math)
  • Re: Probability of picking a positive rational number at random
    ... Classical probability is more limited than measure-theoretic ... there are infinitely many distributions satisfying that relation. ... distributions over all well-orderings of distributions over natural ... natural numbers, in a bijection to the unit interval of reals, by ...
    (sci.math)
  • Re: Probability of picking a positive rational number at random
    ... all uniform distributions over all well-orderings of distributions ... uniform distribution over reals to one over naturals, ... bijection to the unit interval of reals, ... ordinals being a non-measurable set, ...
    (sci.math)
  • Re: .999... ?= 1
    ... >> Why are you bothering mathematicians then? ... > the distributions would also make sense with the restriction to IR+. ... the positive reals, some to denote the nonnegative reals ...
    (sci.math)
  • Re: Question about "distributions" (generalized functions)
    ... "generalized functions" (such as the Dirac delta) as linear ... functions are called "distributions," and if this naming of such ... Measures (and thus probability distributions) already include the Dirac ...
    (sci.math)