Apparently there is a lot of discussion out there as to the validity of this statement. The main argument for equality goes something like this. Say x = 0.99999… (or commonly expressed as .9). Multiply both sides by 10 and you have 2 equations that you can subtract from each other.
10x = 9.9999999... - x = 0.9999999... ------------------- 9x = 9
Reduce the result and now you have x = 1, but as we expressed earlier, x = 0.99999, so 0.99999… = 1. Simple enough, right?
Check out all of the discussion here, here, and and some false counter-examples here.
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