Re: Cantor Confusion

On 12/1/2006 9:35 PM, Virgil wrote:
In article <1164982199.959381.134510@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Eckard Blumschein schrieb:


I recall being a little boy wondering when I was told that while there
is no evidence proving the existence of god there is also no evidence
showing his non-existence. Are those crippled who don't believer in CH?
I consider the background of CH given in the difference between number
and continuum. This might be crippled down to the truth? Do you agree?

No, I am sorry, I do not. The continuum is nothing but our failure to
look closely enough. In physics it lasted 2000 years to settle the idea
of the atom and to supplement and complete it by the uncertainty
relations. The majority of matematicians is not yet far sighted enough
to recognize the same situation in their realm.


We do not yet /know/ that the physical universe is not continuous, so
why should we reject a mathematically continuous real number system?

I do not just agree. I would even like to stress once again that the
mathematical concepts of continuum is independent from its application.
What about continuous real numbers, I only vote for a little bit more
honesty and more consequent reasoning. If irrational numbers are thought
to complete the rationals which sounds quite logical, then the
constituted entity of the reals has to be as fictitious as the
irrationals. The name real "numbers" is misleading due to lacking
trichotomy in this case. Nonetheless, one may largely operate with the
real "numbers" AS IF they were actually numbers. Likewise oo ist often
treated like a number while oo + a = oo obviously violates the ordinary
rules.

.

Relevant Pages

  • Re: The Numerical and the Intuitive Continuum
    ... that the perceptual continuum and the set of reals are disparate, ... perceptual continuum yields the reals. ... point to keep it fixed and non-moving, it takes two arrows to indicate ...
    (sci.math)
  • Re: Why real numbers and points cant model continuum
    ... Continuum, or are "a" continuum. ... not a model of it but the reals ... one must accept his intuitions, in a sense "work within his ... to find a flaw in classical mathematics he must first learn it! ...
    (sci.math)
  • Re: CH yet again.
    ... | [AD implies] that every uncountable set of reals has a perfect subset ... | of a set of reals "defying CH". ... a continuum or countable, as long as that conjecture is necessary ...
    (sci.logic)
  • Re: Interval in a continuum is a fractal
    ... interval also has a non-zero extent or magnitude or span which is ... I grant that Venkat Reddy is not always clear but I don't understand ... construction of the continuum and the spatial/temporal continuum are ... When Cantor and Dedekind constructed the reals as an numerical model ...
    (sci.math)
  • Re: Wheres respect? was Re: Corrective interpretation of real numbers
    ... > Turnabout is fair play. ... A constant function defined on the reals is continuous. ... It's a continuum, it's continuous. ...
    (sci.math)