Mathematics and Applied Mathematics
March 30, 2021
A critique of the hypothesis of the actual infinity
From different areas of mathematics, such as set theory, geometry, transfinite arithmetic or supertask theory, in this book more than forty arguments are developed about the inconsistency of the hypothesis of the actual infinity in contemporary mathematics. A hypothesis according to which the uncompletable lists, as the list of the natural numbers, exist as completed lists. The inconsistency of this hypothesis would have an enormous impact on physics, forcing us to change the continuum space-time for a discrete model, with indivisible units (atoms) of space and time. The discrete model would be a great simplification of physical theories, including relativity and quantum mechanics. It would also suppose the solution of the old problem of change, posed by the pre-Socratics philosophers twenty-seven centuries ago.