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2021-01-04, 04:00   #77
SarK0Y

Jan 2010

2·43 Posts

Quote:
 Originally Posted by VBCurtis 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"?
so $\ln(x)$ and $\frac{d\ln(x)}{x}$ do not exist, right?
Quote:
 Originally Posted by VBCurtis 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"?
Oh, boy, really?
$\lim_{n \to \infty}\left(1-\frac{1}{10^{n}\right)\eq0.9999..99$

Last fiddled with by SarK0Y on 2021-01-04 at 04:10