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Zooming in on infinitesimal 1?.9.. in a post-triumvirate era
Article
Jul 2010
Karin Usadi Katz
Mikhail G. Katz
The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis“...” in the real formul...
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A strict non-standard inequality .999... < 1
Article
Dec 2008
Karin Usadi Katz
Mikhail G. Katz
Is .999... equal to 1? Lightstone's decimal expansions yield an infinity of numbers in [0,1] whose expansion starts with an unbounded number of digits "9". We present some non-standard thoughts on the ambiguity of an ellipsis, modeling the cognitive concept of generic limit of B. Cornu and D. Tall. A choice of a non-standard hyperinteger H specifie...
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