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Old 2021-01-04, 04:00   #77
SarK0Y
 
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Jan 2010

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Quote:
Originally Posted by VBCurtis View Post
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 View Post
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
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