Infinitesimal Unit of Measurement This is just a question that popped into my head which I lack the knowledge to answer (or even to know whether there is an answer, honestly). Does the idea of an infinitesimal unit of measurement even make sense theoretically? If I had a line segment, could it be of infinite length when measured in such units?

The answer is affirmative. Thus, the unit interval $[0,1]$ can be partitioned into $H$ subintervals of infinitesimal length. These are called hyperfinite partitions. Wallis in fact used the symbol $\infty$ in the sense of $H$ above but today it is not customary to use it this way so I used $H$ instead (Wallis was the one who introduced the infinity symbol in the first place).
