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).
For an infinite line segment, its length is infinite inches, infinite kilometers, infinite parsecs, or infinite angstroms - all are same. Angstroms and light-years does not make any difference as infinity + infinity = infinity * infinity = infinity

As infinity is not a number but a concept, it cannot be compared with any real number. A crude definition of infinite is 'a number larger than the largest real number' is also mathematically senseless. 

Einstein said nothing is infinite except the universe and human stupidity.