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Finiteness Notions In Fuzzy Sets, Lawrence Stout Nov 2001

Finiteness Notions In Fuzzy Sets, Lawrence Stout

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Finite sets are one of the most fundamental mathematical structures. In the absence of the axiom of choice there are many different inequivalent definitions of finite even in classical logic. When we allow incomplete existence as in fuzzy sets the situation gets even more complicated. This paper gives nine distinct definitions of finite in a fuzzy context together with examples showing how the properties of the underlying lattice of truth values impact the meanings of finite.


There Really Are No Contradictions: A Response, Calvin Jongsma May 2001

There Really Are No Contradictions: A Response, Calvin Jongsma

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Response to "There are no Contradictions" by T.G. Ammon in The College Mathematics Journal, Vol. 31, No. 1 (Jan., 2000), pp. 48-49 which was part of the "Fallacies, Flaws, and Flimflam" column edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.