Today I worked on exercises from both the review of conics and Analysis with an Introduction to Proof. I also thought some more about the questions from my post About Division. I’ve come up with a new argument that repeating decimals must represent rational numbers. It doesn’t require any theorems about geometric series, but it is going to be a bit of a pain to formalize. I may decide just to give an example of the maneuver it is based on and wave my hands for the generalization. Today I was going to share my proof that the decimal representations of rational numbers must repeat, but it is taking longer than I expected to write that up, so I will have to wait until tomorrow. Stay tuned, faithful readers!
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Adoring this reply.
This faithful reader is staying tuned. (And charmed that such an ancient expression is still used. Can it be understood?) It’s wonderful to see you willing and able to work on this problem with such focus and determination, and to recognize its importance. Good show!
Don’t touch that dial!
I am glad to find myself willing and able. I’ve even been doing some of these investigations without recourse to the CBD, which is encouraging.