>>16586529
>The real number corresponding to a decimal representation f
>f
> is the limit of the series Σ∞z=−sup({z∈Z|f(z)≠0})10−z∗10
>Σ
>z
>=
>−
>s
>u
>p
>(
>{
>z
>∈
>a
>|
>f
>(
>z
>)
>≠
>0
>}
>)
>∞
>10
>−
>z
>∗
>10
> counting down from the highest decimal place. Aka the definition that everyone always gives in 0.9999 =/= 1 threads, and also the inverse of your function if you consider it a map RZ{0...9}
>R
>
>a
>
>{
>0...9
>}
>, if you restrict my function's domain to the image of your function (the mapping from decimal to real is not injective, because, for example, 1 and 0.9999... are the same number).
So you agree with me that 0.999... does not correspond to a real number using the function I provided? Mind you your function works backwards, it assigns to every digit representation some real number, but that is not how real numbers are defined. Real numbers are defined by dedekind cuts and from those definitions we build out digit representations not the other way around.

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Why is lim x=>0 of 1/x equal to infinity instead of undefined? I thought that a quantity that infinitely approaches a certain number is equal to…