YBM
Posts:
277
Registered:
11/27/09
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Re: Matheology § 162
Posted:
Nov 26, 2012 3:47 AM
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Le 26.11.2012 07:38, WM a écrit :
> On 26 Nov., 00:56, Virgil <vir...@ligriv.com> wrote:
>> In article
>> <f6cde06f-8269-4768-a73e-9219bd020...@k6g2000vbr.googlegroups.com>,
>>
>> WM <mueck...@rz.fh-augsburg.de> wrote:
>>> Matheology 162
>>
>>> About limits of real sequences.
>>
>>> The limit of an infinite sequence (a_k) of real numbers a_k is
>>> determined solely by the finite terms of the sequence. Otherwise, the
>>> limit 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 the
>>> real numbers the sequence
>>> 0.1, 0.11, 0.111, ...
>>> has the limit 0.111... = 1/9.
>>
>> Unless we are give some assurance that the pattern that most of us see
>> is the intended one, such as by formula, no one can state "THE" limit,
>> as no such limit exists.
>
> Study real analysis. There are plenty of sequences which have one and
> only one accumulation point. That is called *the* limit.
What is properly amazing, and shamefull, is that WM is actually teaching
math in an academic german institution while confusing having several
accumulation points for a sequence (for a given topology) and having
different limits for different topologies.
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