May 15th, 2017, 10:17 AM  #61  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
These are the sort of questions that people ask, but we should be telling them that they are the wrong sort of questions. Real numbers are not a product of the decimal system, the decimal system is a product of real numbers. Real numbers are limits. Nobody who understands limits questions that $$\sum_{n=0}^n \frac1{2^n} =2$$ So there is no reason why anyone who understands limits should fail to understand that $$0.999\ldots = \sum_{n=1}^n \frac9{10^n} =1$$ Perhaps, as Maschke says, the best solution for those that don't understand limits is to say: Quote:
 

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