You Can Hardly Imagine a Rolling Wheel

I was asked a middle school physics homework problem by a "bear kid". Jim was holding one end of a plank, and the other end of the plank was placed on a cylinder as shown in the figure (OK, let's not focus on why he had to do that). Jim pushed this...

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Why is 0.999... equal to 1

So, why is 0.999... equal to 1? This wiki page has given an answer:  in fact, 0.999... and 1 are different representations of the same number. It seems not intuitive at all: 0.999... does look less than 1 to a very very tiny extent....

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