The idea of the unreachability of continuum from discretion by serial process has a distinguished (if decidedly marginal) history.
The most distinguished exponent IMO was Hermann Klaus Hugo Weyl.
http://www-gap.dcs.st-and.ac.uk/~his...ians/Weyl.html
bio Hermann Weyl
A taste of Prof. Weyl's criticism of the Dedekind-Cantor procedures might be found in his book:
The Continuum : A Critical Examination of the Foundation of Analysis
Dover; reprint edition (1994)
Here is a more recent review of Weyl's ideas:
http://publish.uwo.ca/~jbell/Hermann%20Weyl.pdf
University Western Ontario - John L. Bell: Hermann Weyl on Intuition and the Continuum
Here is another prominent exponent:
http://www-gap.dcs.st-and.ac.uk/~his...s/Brouwer.html
bio Luitzen Egbertus Jan Brouwer
Weyl discusses the Brouwer procedure in another book:
Philosophy of Mathematics and Natural Science
Atheneum; reprint edition (1949)
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Possible interesting collateral: fuzzification.
http://www.wikipedia.org/wiki/Fuzzy_logic
Wikipedia: fuzzy logic
http://plato.stanford.edu/entries/logic-fuzzy/
SEP: fuzzy logic
http://www.wikipedia.org/wiki/Fuzzy_sets
Wikipedia: fuzzy sets
http://www-2.cs.cmu.edu/Groups/AI/ht...part1/faq.html
fuzzy FAQs
fuzzy arithmetic?
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