grei
Posts:
97
Registered:
11/27/12


Re: How does infinitesimal exist?
Posted:
Apr 11, 2013 10:08 AM


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 "PreCalculus" 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.

