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Topic: How does infinitesimal exist?
Replies: 21   Last Post: Jun 7, 2013 12:13 AM

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Posts: 132
Registered: 11/27/12
Re: How does infinitesimal exist?
Posted: Apr 11, 2013 10:08 AM
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Completely wrong. It is not just that "the last digit is difficult to write", there is NO "last digit". A numeral such as 0.999... represents the sum of an infinite series: .9+ .09+ .009+ .0009+ ... That sort of series is handled, in general in Calculus but special cases are seen in "Pre-Calculus" or "Intermediate Algebra".

.9+ .09+ .009+ ... is, in particular, a "geometric series". It can be written .9(1+ .1+ .01+ .001+ ...)
which is of the form a(1+ r+ r^2+ r^3+ ...) with a= .9 and r= .1.

And, it can be shown that the sum is equal to a/(1- r).
(Not "approaching" that, the sum is EQUAL to it.)

Here, that would be (.9)(1- .1)= .9/.9= 1.

0.9999.... is exactly EQUAL to 1.

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