If you can't find a number between 0.999... and 1, are they the same?

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d_leet said:
It definitely does not show that 0.9999=1, .9999 = 9999/10000 which is not equal to one, but if we take the notation that .999... represents the infinite geometric series with .9 as the first term and 1/10 as the common ratio then this is equal to one .999... = 1.

I wanted to say 0.9999...
I always talked about 0.9999... but i forgot the ... because that's not the notation I learned.
I learned that if you want to write...let's say 0.6767 repeating you write
0.(67) in parenthesys like that. But you all use the ... instead so I tried to use yours but at times I forgot it.

0.9999 is a banality to convert...also an irrelevance.
However 0.(9) using the method I did with the long number as example would look like this:

(the whole number - the non-repeating number)/as many 9s as different repeating decimals followed by as many zeroes as the decimals not repeating.

So...

(09-0)/9 is just 9/9 or 1.