Re: .999... ?= 1

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 06/08/04 

Date: Tue, 08 Jun 2004 07:20:59 +0100

Herman Jurjus wrote:

>>>>I see zero having three aspects of equal value but different sign:
>>>> minus 0.0 over bar
>>>> just zero
>>>> plus 0.0 over bar.
>>>
> [snip]
>
>>>>Both the negative and the positive description, from the left and from
>>>>the right, respectively are identical with just zero.
>>>
> [snip]
>
>>Do not consider it an attack on
>>numbers like 0 and 1 if I try to add some subtleties. Since language of
>>mathematics has failed for centuries to satisfactory resolve the
>>issue, it might be worth pondering about alternatives. What does +0
>>mean? How does it differ from -0? We agree about the identity of their
>>value zero, no matter whether it is seen from the left or from the right.
>
>
> Do you happen to know the book "Inconsistent
> Mathematics", by Chris Mortensen?

The title sounds interesting. Our library doesn't have it.

> The function such that f(x) = 0 for x < 0 and
> f(x) = 1 for x > 0 can be turned (according to the
> book) into a _continuous_ function, by defining
> both f(0) = 0 and f(0) = 1.

That is exactly what practice sometimes needs but gospel-like tenets do
not allow.

> The rather flagrant
> contradiction ( 0 = f(0) = 1 ) is made harmless,
> by using a non-standard logic (a 'paraconsistent'
> logic = logic in which the ex-falso-quodlibet rule
> fails).

If I recall correctly, quodlibet means whatever. People used to obey the
  ban of division by zero. Why don't they accept that other rules also
fail at the infinitely small.

> They claim this leads to very handy calculus
> rules in applied situations.
>
> Is this close to what you have in mind?

Perhaps it is, at least as concerns the practical needs.

Thanks and Regards,
Eckard Blumschein

Relevant Pages

  • Re: Bobby Fischers Conquest of Everest..
    ... attended Robin Wilson?s talk a few months ago about zero in mathematics ... more important and pivotal in all sorts of ways of thinking about the ... the void and the vacuum that we?re familiar with. ...
    (rec.games.chess.misc)
  • Re: Bobby Fischers Conquest of Everest..
    ... attended Robin Wilson?s talk a few months ago about zero in mathematics ... more important and pivotal in all sorts of ways of thinking about the ... the void and the vacuum that we?re familiar with. ...
    (rec.games.chess.misc)
  • Re: The annotated annotated annotated C standard
    ... outside the Standard in order to achieve a platform-specific goal. ... mathematics found itself ... it is true that there are some cases where division by zero ...
    (comp.programming)
  • Re: The annotated annotated annotated C standard
    ... outside the Standard in order to achieve a platform-specific goal. ... mathematics found itself ... it is true that there are some cases where division by zero ...
    (comp.programming)
  • Re: .999... ?= 1
    ... the meaning of a number it might be premature to exclude the possibility ... For instance zero ... much of decimals (or alternatively an overbar even in case of omitted ... Now we are at the roots of mathematics. ...
    (sci.math)