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Transfinite Numbers.

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Posted by Paul R. Martin on December 9, 2001 02:25:44 UTC

Hi Mark,

Here's some thoughts on your post.

>>>Mathematicians had a hard time swallowing the idea of "as close to zero as you can possibly get without actualy being zero".>However, dx, is nonetheless a common term in differential calculus. It is an infinitessimal increment, and for all practical purposes, equal to zero (about as close as you can get without actualy "being").>>But perhaps we can define "zero" within the context of George Cantor's transfinite numbers...(??)Perhaps just as zero is indivisible, or "infinitely small", there can be different cardinalities of "infinitessimals".

This way aleph-nought does indeed have a reciprocal. The reciprocal of the first order of infinite happens to be "almost zero but not just quite".>1 - .9999999 = "almost zero but not just quite".>It can be shown that 1 - .99999 can be made to be smaller than any arbitrary real number>>just as infinite can be shown to be larger than any arbitrary real number (which is the definition of "infinite").

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