Thats the thing... you can not depict infinity graphically or by writing a large number. So you are correct in the sense that you can't plot a coordinate system and show infinity. You can only depict finite graphs and numbers. And for every finite number 0.999999......9 there is a solution of a number 0.0000001
But 0.9999.....9 is not equal to 0.9 period, no matter how many 9s you add. And there is no last digit. Because even the number 1 can be depicted as 1.00000000 with infinite 0's.
Look at this problem from this point of view.
We think that 0.9 period + A = 1
We assume that A is something like 0.0000000000000000...00001. How can we express this number? (10^-oo). And what is the value of 10^-oo? 0
What is the value of 10^-(100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)?
Although the number is extremely small, but it is not 0. And I can add finetely more 0's and it would still be > 0.
10^-oo = 0 and 0.9 period = 1.
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