This is a common "debate" on internet forums. I tried to see if it was on these forums, but I couldn't find it. Anyway, what always surprises me is how much it bothers people, especially because equations like 0.333... == 1/3 don't seem to. I want to know why that is.
My theory is that people learn about repeating decimals in grade school. Repeating decimals come out of the division algorithm they're taught. That algorithm "is division" and whatever it produces is the right answer. The algorithm works for numbers like 1/3, but doesn't work for 1/1 (it terminates immediately instead of generating a repeating decimal). Since the algorithm fails to produce 0.999... from 1/1, the equation seems wrong and unnatural.
What do you think?
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