Euclid s axioms vs Zeno s paradoxes of infinite regress Euclid wins.
Infinity is banished.
Kepler brings back concept of infinitesimal for convergence to a limit as infinity is approached, but infinity itself is still banished. The infinite is but a fa on de parler, meaning a limit to which certain ratios may approach as closely as desired when others are permitted to increase indefinitely. Later Lebesgue, Hausdorf and others invent new measurements. Hilbert invents his own fractal, but also declares search for axiomatic proof of the completeness of all mathematics. No one can expel us from the paradise created by Cantor.