Hello people, heres my worthless two cents.

1 does IN FACT = 0.9 (recurring).

BUT

1/3 does NOT = 0.3 (recurring)

I'm sorry, It just doesn't. Go read a further maths text book.

ACTUAL PROOF would be something like this:

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lets say x=0.9 recurring.

therefore 10x = 9.9 recurring.

and if we do 10x - x = 9,

therefore x = 1

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There is absolutely no flaw in that.