Note 4 — Chapter I · MANIFOLDS
Reading edition
The discoveries of du Bois Reymond have shown that we could proceed still further and interpose an indefinite number of additional points, but in the present state of mathematics this extension is viewed only as a mathematical curiosity. We may mention, however, that the rejection by Hilbert of the axiom of Archimedes (to be discussed in the following chapter), leading as it does to the strange non-Archimedean geometry, would be equivalent to considering the mathematical continuum as of this more general variety.