Its a simple argument that tries ot be rigorous. If I don¨t agree with it I must disagree with some part of it. When I go step by step over it there is a suspicious step.
The proof assumes/states that 9.99999… −0.999999 = 9. I am unconfident with operations on infinite decimal place decimals that I am not sure that I agree. 9.99999… −0.9999 could also be 8.00...009. In particular I don’t know whether you get the same object if you mulitiply 0.9999… by ten or if you set the first zero equal to 9.
Understanding to agree with how the proof handles is to be proficient on what reals are and the technicalities and to understand that reals are what is meant.
Havinga standard that things are not real if they can’t be realised in reals would make i and complex numbers to be “unintelligble”.
Its a simple argument that tries ot be rigorous. If I don¨t agree with it I must disagree with some part of it. When I go step by step over it there is a suspicious step.
The proof assumes/states that 9.99999… −0.999999 = 9. I am unconfident with operations on infinite decimal place decimals that I am not sure that I agree. 9.99999… −0.9999 could also be 8.00...009. In particular I don’t know whether you get the same object if you mulitiply 0.9999… by ten or if you set the first zero equal to 9.
Understanding to agree with how the proof handles is to be proficient on what reals are and the technicalities and to understand that reals are what is meant.
Havinga standard that things are not real if they can’t be realised in reals would make i and complex numbers to be “unintelligble”.