Re: Epistemology 201: The Science of Science

From: aeo6 (aeo6_at_cornell.edu)
Date: 03/14/05 

Date: Mon, 14 Mar 2005 11:49:10 -0500

Lester Zick said:
> 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.
Look at it instead as, "how many zeroes can I fit in this finite number?", not,
"How many zeroes must I add to equal this finite number?" Then, you will see
the answer's always infinite.
>
> > 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.
The unit infinity is the multiplicative inverse of the unit infinitesimal.
>
> Regards - Lester
> 

-- 
Smiles,
Tony

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... Lester Zick said: ... > subtraction and when you subtract 0 you aren't subtracting anything. ... > definition for zero as the difference between a thing and itself. ... The unit infinity is the multiplicative inverse of the unit infinitesimal. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... Lester Zick said: ... > subtraction and when you subtract 0 you aren't subtracting anything. ... > definition for zero as the difference between a thing and itself. ... The unit infinity is the multiplicative inverse of the unit infinitesimal. ...
    (sci.physics)
  • Re: infinity
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  • Re: John Gabriels Theorem Revisited.
    ... w/n can never be zero, no matter how large you make n. ... The difference between zero and infinity is that we can perform finite ... in his proof is the use of what he calls positional derivatives. ... average sum and average tangent theorem. ...
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  • Re: You Dont Have to Be Nuts to Be a Mathematician ...
    ... Extended from minus infinity to plus infinity. ... a universal meaning of numbers and in particular of zero. ... > neutral zero between positive and negative numbers. ... > must be fundamentally revised in order to purify mathematics from some ...
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