Abstract
Contrary to common opinion, the question “what is the continuum?” does not have a final answer (Bell, 2005), the immortal work of Dedekind notwithstanding. There is a deeper answer implicit in an observation of Euler. Although it has often been dismissed as naive, we can use the precision of the theory of categories to reveal Euler’s observation to be an appropriate foundation for smooth and analytic geometry and analysis.
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Lawvere, F.W. (2011). Euler’s Continuum Functorially Vindicated. In: DeVidi, D., Hallett, M., Clarke, P. (eds) Logic, Mathematics, Philosophy, Vintage Enthusiasms. The Western Ontario Series in Philosophy of Science, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0214-1_13
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DOI: https://doi.org/10.1007/978-94-007-0214-1_13
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