# Zooming in on infinitesimal 1–.9.. in a post-triumvirate era

@article{Katz2010ZoomingIO, title={Zooming in on infinitesimal 1–.9.. in a post-triumvirate era}, author={Karin U. Katz and Mikhail G. Katz}, journal={Educational Studies in Mathematics}, year={2010}, volume={74}, pages={259-273} }

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 formula $\hbox{.999\ldots = 1}$. Infinitesimal-enriched number systems accommodate quantities in the half-open interval [0,1) whose extended decimal…

## 30 Citations

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We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations…

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