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Abigor Anathema
Veritasium
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Comments by "Abigor Anathema" (@kruksog) on "Something Strange Happens When You Keep Squaring" video.
You should really use a better argument to show that .9 repeating is 1. For example, that if it isn't 1, there exists a real between .9 repeating and 1, by the density of the reals. It's just very easy to fall into circular arguments via the "proof" you used. In your argument, you need to show that 0.9 repeating times 10 is 9.999... That is certainly true, but showing that to be the case reduces to showing that 0.9 repeating is 1. I think you can see how the argument is beginning to get circular. Anyway, nice video.
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