There is NO proof that 0.999...=1
No.11870856 ViewReplyOriginalReport
Quoted By: >>11870870 >>11870940 >>11870943 >>11870946 >>11870977
>1/3=0.333...
>3/3=0.999...
Wrong, this assumes you accept an axiom which you dont have to
>"proof" via dedekind cuts
Not real
>"proof" via cauchy sequence
Not real
I would concede that 0.999...=1 if only it could be properly represented in the decimal format (which it is not). 0.999... is an infinitely repeating decimal sequence, and infinity isnt a number, it is a concept. The limitations of decimal notation prevent the sequence from ever terminating, as even though it is a set value that is infinite, the theoretical final digit will always be 9, and it is impossible to add the 1/10^n value needed for it to equal 1. Therefore, 0.999... has no meaningful answer.
>3/3=0.999...
Wrong, this assumes you accept an axiom which you dont have to
>"proof" via dedekind cuts
Not real
>"proof" via cauchy sequence
Not real
I would concede that 0.999...=1 if only it could be properly represented in the decimal format (which it is not). 0.999... is an infinitely repeating decimal sequence, and infinity isnt a number, it is a concept. The limitations of decimal notation prevent the sequence from ever terminating, as even though it is a set value that is infinite, the theoretical final digit will always be 9, and it is impossible to add the 1/10^n value needed for it to equal 1. Therefore, 0.999... has no meaningful answer.
