Re: hot to write out this summation:

On 7/1/2024 10:12 AM, Moebius wrote:

Am 01.07.2024 um 18:45 schrieb Chris M. Thomasson:

On 6/30/2024 3:44 PM, Mike Terry wrote:

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[...] you didn't put quotes around anything, making it look like you were describing regular real numbers, but regular real numbers have decimal notation with digits (after the decimal point) just at positions 1,2,...n,... with n < w.  So a "string" like .(0)(1) does not represent a real number. And "taken to infinity" /as a sequence of real numbers/ your sequence obviously converges to the real number 0.

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Well, humm... Each iterate of .(0)(1) is a real number as in:

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Well, ".(0)(1)" is an undefined expression in the present context. It doesn't mean anything sensible (especially no real number).
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r[0] = .01
r[1] = .0011
r[2] = .000111
r[3] = .00001111
...
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Each one is a real number, and <etc.>

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And r[n] "tends to" 0 (=0.000...) as n "tends to infinity".
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In other words, r[n] --> .(0) for n --> oo.
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Again, r[n] DOES NOT tend to something that is denoted by ".(0)(1)" (see Mike comment above). Only in Mückenland (i.e. crankland) 0.999... can also be written as "0.999...999".

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 I do not want to be akin to a crank! Yikes!
 I was just thinking that each iterate of the .(0)(1) is a real number... Is that a bad way to ponder on such things?