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how does .999 and so on = 1? Calculus: limits

 
 Sep 15, 2021
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Let x = 0.999... etc.

Then 10x = 9.999... etc.

 

Subtract:  10x - x = 9.999... - 0.999...

 or                 9x = 9

so                   x = 1

 
 Sep 15, 2021

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