Re: The Jesus Exegesis

David DeLaney <dbd@xxxxxxxxxxxxxxxxxx> wrote:
Bill Snyder <bsnyder@xxxxxxxxxxx> wrote:
Gene <gene@xxxxxxxxxxxxx> wrote:
William Hyde <wthyde1953@xxxxxxxxx> wrote in news:9a85e0cd-
The key is in the word "infinitesimal" which in this case does
not mean "very, very, small" but means "arbitrarily small but
not zero".

A positive infinitesimal is not arbitrary small, but is smaller
than any positive real.

And yet positive reals may be found arbitrarily close to zero.

Yep. Which means that, considered in relation to what people "know" about
real numbers, infinitesimals are at least somewhat Weird, and the rules they
play by don't always extend back into the real numbers intuitively.

Another way to think about it is by visualizing real numbers as a mesh, and
infinitesimals as a mesh with much finer weave...

ObSF, since as near as I can tell, though I'm missing about half the posts
in this thread for some reason, it's only posted to r.a.sf.w: Rudy Rucker's
_White Light_ and the various descriptions of the transfinite side of Cim\"on.

Dave
--
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It's not the clock that slows the hour The definition's plain for anyone to see
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.

Relevant Pages

  • Re: rational or irrational?
    ... These infinitesimals do not have a decimal representation. ... exist in the reals. ... just because there are everywhere reals between zero ...
    (sci.math)
  • Re: how to list all of the real numbers
    ... of an infinite set by the axiom of infinity as generally stated (that ... maps the first integer after zero to the first real number after zero ... in the total linear and well-ordering there of the reals, ... With regards to the notions of infinitesimals and where they exist the ...
    (sci.math)
  • Re: The Jesus Exegesis
    ... And yet positive reals may be found arbitrarily close to zero. ... mesh, and infinitesimals as a mesh with much finer weave... ...
    (rec.arts.sf.written)
  • Re: infinity
    ... > infinitesimal reals between zero and one, ... > and only reals between zero and one. ... What do you mean "trichotomous infinitesimals"? ...
    (sci.math)
  • Re: Non-zero gaps between real numbers
    ... The infinitesimals pack the surreal line ... with greater density than the reals. ... Are they a gap in reality? ... numbers with zero gap between them. ...
    (sci.math)
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