User blog comment:Edwin Shade/Numbers As Big As Infinity/@comment-25337554-20171115092545

First, I have to say that there are numbers called "p-adic numbers," which extend forever to the left (reverse of the real numbers).

Then, we can say that your "number" is actually a pair of a real number and a p-adic number because the leading and trailing digits are so "distinct" that they don't interact each other.

Anyway, as is often, the next step must be arithmetic. There should be addition and multiplication, and eventually you can make a whole new number world!