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Old 2021-01-04, 00:38   #74
VBCurtis's Avatar
Feb 2005
Riverside, CA

12A716 Posts

Originally Posted by SarK0Y View Post
0.9 < 0.99 < 0.999< .. < 0.999..99 it's continuous sequence/function. if you assume it can reach its final point 1 then you fall into bad situation like..
\lim_{x \to 1}\frac{1}{1-x}\eq \frac{1}{0}
Neither side of your limit example exists, so your congruence is nonsensical- and irrelevant to whether 0.9-repeating is equal to 1.

There is no sequence involved in the single number 0.9-repeating, either. I didn't ask about 0.9, nor 0.99. 0.9-repeating is neither of those numbers. Every member of your sequence is strictly less than 0.9-repeating, anyway.

You might figure out the flaws in your reasoning if you used words properly- how do you define "continuous sequence"?
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