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A simple question.
#51
RE: A simple question.
(March 15, 2011 at 6:06 pm)Zenith Wrote: By the same logic I can say that 0.(1) = 0.11...111 is finite because it ends with "1".
A few things wrong with this statement:

1) 0.11...111 would be finite even if it didn't end with a 1, since I can name a number higher than it (0.2), and hence it is not infinite. What you mean is that it is finitely long, which is perfectly true if it ends with a 1, and the way you have written it (0.11...111) shows this.

2) 0.(1) is not the same as 0.11...111, since by definition 0.(1) doesn't have an end, and 0.11...111 has a very visible end. The correct notation for 0.(1) is 0.111... (the ellipsis indicating that the 1 repeats endlessly).

3) Whilst 0.11...111 does end with a very visible 1, 0.(1) or 0.111... does not. The ellipsis makes it endless, and so whilst it is a finite value, it is not of finite length.

Quote:In other words, my example hasn't an end by definition, either. If this "0.00...001" does not look as you'd like, then use this representation:

"1/10 * 1/100 * 1/1000 ..." - because this is clearly not an "invalid" thing.
Your example does have an end: 0.00...001 <-- there it is.

Whilst your calculation is a valid one, the answer to it diverges to 0 as I pointed out, and as such it is not a valid answer to the question "what is the first number that comes after 0?" because either (a) it eventually becomes 0, or (b) it diverges to a value which is impossible to calculate (since we would need a infinite amount of time in order to do it).

Quote:I don't care if infinite geometric series use or not the infinity in the actual calculation. I also don't care how this thing should be called. But, if you insist that "1/10 * 1/100 * 1/1000 ..." must not be used, perhaps you can show where it's written that this thing is forbidden to be used.
I never insisted that your calculation must not be used, I said that the calculation diverges to 0, which in mathematics either means it becomes equal to 0, or becomes infinitely small and cannot be calculated.

I asked you what the first number to come after 0 was, and you have not given me a valid answer.
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Messages In This Thread
A simple question. - by Tiberius - April 11, 2010 at 10:58 pm
RE: A simple question. - by tavarish - April 11, 2010 at 11:28 pm
RE: A simple question. - by Dotard - April 11, 2010 at 11:29 pm
RE: A simple question. - by The_Flying_Skeptic - April 11, 2010 at 11:29 pm
RE: A simple question. - by theblindferrengi - April 11, 2010 at 11:48 pm
RE: A simple question. - by Tiberius - April 11, 2010 at 11:56 pm
RE: A simple question. - by Violet - April 12, 2010 at 7:06 am
RE: A simple question. - by Dotard - April 12, 2010 at 7:40 am
RE: A simple question. - by Tiberius - April 12, 2010 at 7:48 am
RE: A simple question. - by Dotard - April 12, 2010 at 8:00 am
RE: A simple question. - by Tiberius - April 12, 2010 at 8:05 am
RE: A simple question. - by Xyster - April 12, 2010 at 8:07 am
RE: A simple question. - by The_Flying_Skeptic - April 12, 2010 at 3:38 pm
RE: A simple question. - by Tiberius - April 12, 2010 at 3:47 pm
RE: A simple question. - by The_Flying_Skeptic - April 12, 2010 at 3:48 pm
RE: A simple question. - by Edwardo Piet - April 13, 2010 at 10:53 am
RE: A simple question. - by Violet - April 13, 2010 at 3:05 pm
RE: A simple question. - by Edwardo Piet - April 14, 2010 at 10:14 am
RE: A simple question. - by Violet - April 14, 2010 at 10:32 am
RE: A simple question. - by Edwardo Piet - April 14, 2010 at 10:42 am
RE: A simple question. - by Violet - April 22, 2010 at 7:59 am
RE: A simple question. - by The_Flying_Skeptic - April 14, 2010 at 12:22 pm
RE: A simple question. - by aufis - April 20, 2010 at 3:25 am
RE: A simple question. - by Tiberius - April 20, 2010 at 8:36 am
RE: A simple question. - by theblindferrengi - April 20, 2010 at 8:55 am
RE: A simple question. - by Zhalentine - April 20, 2010 at 9:12 am
RE: A simple question. - by Tiberius - April 20, 2010 at 9:25 am
RE: A simple question. - by aufis - April 22, 2010 at 2:35 am
RE: A simple question. - by Tiberius - April 22, 2010 at 7:31 am
RE: A simple question. - by Tiberius - April 22, 2010 at 8:05 am
RE: A simple question. - by Violet - April 23, 2010 at 6:33 pm
RE: A simple question. - by The_Flying_Skeptic - April 23, 2010 at 7:03 pm
RE: A simple question. - by Violet - April 24, 2010 at 5:26 am
RE: A simple question. - by aufis - April 23, 2010 at 3:02 am
RE: A simple question. - by Tiberius - April 23, 2010 at 10:15 pm
RE: A simple question. - by Zenith - March 11, 2011 at 10:06 pm
RE: A simple question. - by Tiberius - March 12, 2011 at 10:46 am
RE: A simple question. - by Zenith - March 12, 2011 at 11:17 am
RE: A simple question. - by Tiberius - March 12, 2011 at 11:57 am
RE: A simple question. - by Zenith - March 12, 2011 at 1:30 pm
RE: A simple question. - by LastPoet - March 12, 2011 at 4:01 pm
RE: A simple question. - by Zenith - March 12, 2011 at 5:07 pm
RE: A simple question. - by LastPoet - March 13, 2011 at 7:24 am
RE: A simple question. - by Zenith - March 15, 2011 at 8:53 am
RE: A simple question. - by Tiberius - March 15, 2011 at 2:22 pm
RE: A simple question. - by Zenith - March 15, 2011 at 6:06 pm
RE: A simple question. - by Tiberius - March 16, 2011 at 7:01 pm
RE: A simple question. - by Zenith - March 17, 2011 at 10:38 am
RE: A simple question. - by Tiberius - March 17, 2011 at 5:02 pm
RE: A simple question. - by Zenith - March 18, 2011 at 1:25 pm
RE: A simple question. - by theVOID - March 15, 2011 at 3:40 pm
RE: A simple question. - by theVOID - March 15, 2011 at 6:20 pm
RE: A simple question. - by Zenith - March 16, 2011 at 4:38 pm
RE: A simple question. - by theVOID - March 16, 2011 at 4:53 pm
RE: A simple question. - by Tiberius - March 18, 2011 at 2:13 pm
RE: A simple question. - by Zenith - March 18, 2011 at 3:30 pm

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