At dinner tonight, these were two of Madison's questions.
1) Have you ever had a theory that someone convinced you was wrong, so you changed your mind, but which then you reworked later and realized that your first theory was right?
2) In response to a discussion about numbers that repeat infinitely in mathematics, like 1/3, she wanted to know if David had ever encountered an example of a number that had an infinitely repeating part, but completely by coincidence, without a mathematical cause.
So, friends, how about #1? Any examples?
As for #2, David says that he has seen some examples, and that he's going to try to work one up for her.
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