Re: Epistemology 201: The Science of Science

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/13/05 

Date: Sun, 13 Mar 2005 18:52:41 GMT

On 13 Mar 2005 17:44:32 GMT, stephen@nomail.com in comp.ai.philosophy
wrote:

>In sci.math Allan C Cybulskie <allan.c.cybulskie@yahoo.ca> wrote:

[. . .]

>: But I'd like to ask you to think for an instant: putting aside the example I
>: just gave WHY can't I subtract infinity from infinity? If infinity is the
>: same size or number, then it should be simple to do so. But if infinity is
>: simply a number for a large amount of various sizes or numbers, then you
>: cannot (obviously) subtract it out, but then your claim that "x + a = x" as
>: a justification of any sort for "they have the same number of elements"
>: cannot work.
>
>Why can you not divide by 0?

Technically you can if you divide 0 by 0 because then L'Hospital's
rule comes into play. But the reason you can't divide some finite
nonzero thing by zero is because division involves repetitive
subtraction and when you subtract 0 you aren't subtracting anything.

> The point is people have defined
>number systems which include an "infinity".

Actually not. People have defined number systems which include a
definition for zero as the difference between a thing and itself. The
idea of infinity is not part of any number system definition because
it just means undefined. People just like to pretend mathematical
definition is arbitrary when it is no such thing, as definitions of
zero, division by zero, and definition of infinites definitely show.

Regards - Lester

Relevant Pages

  • Re: X/0 DEFINED
    ... > times that we may subtract the denominator from the numerator to the ... > Infinity has a comlex meaning, with at least two separate underlying ... > power of multiplication by zero, thus allowing some X other than zero ...
    (sci.math)
  • Re: Checking for Undefined [was Re: Ada vs Fortran for scientific applications]
    ... infinity (e.g., divide a non-zero number by zero) and plus or minus ... fyi, Matlab supports NAN's, and it has Inf and -Inf ...
    (comp.lang.fortran)
  • X/0 DEFINED
    ... times that we may subtract the denominator from the numerator to the ... The usual argument against this is that if X/0 = Infinity, ... power of multiplication by zero, thus allowing some X other than zero ...
    (sci.math)
  • Re: zero and infinity
    ... > Infinity is not a number. ... > You cannot divide by something that is not a number. ... Where on earth did you get the strange idea that zero is some sort ... Zero / zero can only equal zero, ...
    (sci.physics.relativity)
  • Re: Im always a winner
    ... Divide by zero in any equation and you get ... so you can't just check it against a NaN you happen to have ... True, but then infinity isn't a number either, ...
    (alt.usage.english)