```Date: Nov 25, 2012 4:37 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 162

Matheology § 162About limits of real sequences.The limit of an infinite sequence (a_k) of real numbers a_k isdetermined solely by the finite terms of the sequence. Otherwise, thelimit would not have to be *computed* but would have to be *created*.Analysis is concerned with analyzing, i.e., with finding.To give an example, we can state with absolute certainty that in thereal numbers the sequence0.1, 0.11, 0.111, ...has the limit 0.111... = 1/9.That is independent of the method which is used to analyze thesequence. But there are different aspects of the limit, namely thenumerical value of the limit, the set of coefficients of the powerseries, its cardinal number, the set of indexes which belong to adigit 1, its cardinal number, the set of indexes which belong to adigit 2, its cardinal number, the set of different digits appearing inthe limit, and many further aspects.If any of these aspects is computed by another than the analyticalmethod and turns out as deviating from the analytical result, then theother method is not suitable for analytical purposes.Regards, WM
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