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Asking what a number (1) minus a non-exising value .9 repeating is meaningless. But if we assume the “infinitiness” of .9 repeating then we must also assume that taking 1 – “this” will equal some infinitely small number that is also greater than 0. This fictitious “number” would be the same as “the smallest real number that’s larger than zero”, which doesn’t exist.

http://en.wikipedia.org/wiki/0.999

An ‘infinitesimal’ is a 17th century idea that was never mathematically rigorous. 200 years later that idea was entirely replaced with the modern definition of a limit.

 

 

 

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