User blog comment:Rgetar/Transfinite decimal fractions/@comment-36718579-20190417170035/@comment-35470197-20190418024320

As I wrote above, such naive extensions of operators do not work. For example, you will notice that 10/ω does not make sense if you require 10/ω = 9/ω + 1/ω.

It is because decimal expressions are not useful to define operators even when we are only dealing with real numbers. (By the way, one of great benefits to use p-adic numbers is that we can define an expression-based operation unlike real numbers.)