 Could that final assumption be questioned? It is (as noted above) a consequence of the Cauchy definition of an infinite sum; however Grünbaum (1967) pointed out that that definition only applies to countable sums, and Cantor gave a beautiful, astounding and extremely influential ‘diagonal’ proof that the number of points in the segment is uncountably infinite. There is no way to label all the points in the line with the infinity of numbers 1, 2, 3, … , and so there are more points in a line segment than summands in a Cauchy sum. In short, the analysis employed for countably infinite division does not apply here.