User blog comment:Rgetar/Transfinite decimal fractions/@comment-36718579-20190417170035/@comment-35470197-20190418010305

@Naruyoko

Usually, such operators do not make sense in expression-based extensions of numbers (e.g. the transfinite decimal expansion by the OP).

On the other hand, there are several ways to formally define such operators for more theory-based extensions of numbers. For example, surreal numbers, which the OP mentioned in the blog post, and numbers in non-standard analysis, which I mentioned in a comment below, admit devision.