A lead-in to ten-adic numbers

Most people are willing to say that 0.9999… (infinitely many nines to the right of the decimal point) is worth contemplating even though we might debate over whether or not the value of this infinitely long decimal is 1. But we do seem to be comfortable playing with infinitely long decimals: 1/3 = 0.333… and 4/7 = .571428571428571428…. in general, with no real qualms or concerns.

But what about infinitely many digits to the left of the decimal point. Is the quantity …99999 worth considering?

Welcome to ten-adic numbers!

This PDF essay is a bit rough, but it is my quick attempt to give a story that leads to and explains ten-adic number arithmetic. We focus it on the work of 1 <--10 machine from the story of Exploding Dots.

Ten-adic Thinking with Exploding Dots

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