Re: .999... ?= 1

From: Lothar Brendel (l.no.spam.brendel_at_uni-duisburg.de)
Date: 06/07/04 

Date: Mon, 07 Jun 2004 19:52:39 +0200

Eckard Blumschein wrote:
> Lee Rudolph wrote:
>
>>> Well, in IR or Q any exact number is a fictitious one in so far it
>>> just occupies an infinitesimal small range between its neighbours.
>>
>> To the extent that this statement is meaningful, it is false.
>
> From the perspective of a number per se your refusal is understandable.
> I did not clearly enough express that I meant the practical localization
> of the position corresponding to an exact number.

I should define a macro for this objection of mine: "practical
localization of the position" is not a mathematical concept. How do you
_define_ it?

Don't you realize that you are constantly talking non-math?

[...]

>>>>> Nobody can give a concrete epsilon being small enough
>>>>> as not to contain infinitely much rather than infinitely many
>>>>> of different real numbers in between the mentioned two real numbers.
>>
>> Your "conclusion" ... is in no sense a logical consequence
>
> Originally, I referred to "The Ghost in the Machine" who wrote on June, 3:
> Fortunately, two real numbers are equal if one can show that
> they are closer than any given epsilon -- and that's easy enough
> to show in this case. (To claim otherwise invites deconstructing
> quite a bit of calculus.)
>
> I realized that a given epsilon has only two pecularities. It definitely
> differs from zero, and it is a given, in other words, a fixed value.
> Maybe the sentence was meant differently. I did not intend to correct it.

This clearly shows that you never really digested something like the
\epsilon-\delta-definition of continuity. The definition said "_any_
given \epsilon", not a fixed one.

ciao
        Lothar