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Re: Matheology § 162
Posted:
Nov 28, 2012 10:01 AM
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On 28 Nov., 14:56, mstem...@walkabout.empros.com (Michael Stemper)
wrote:
> In article <f6cde06f-8269-4768-a73e-9219bd020...@k6g2000vbr.googlegroups.com>, WM <mueck...@rz.fh-augsburg.de> writes:
>
> >Matheology =A7 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.
>
> That is correct. Since the a_k are chosen from the real numbers, and since
> all real numbers are finite, all of the a_k are finite, and the sequence
> has no infinite terms.
>
> Now, depending upon the nature of the sequence, the terms may increase
> without limit, which is one way of having a real sequence that has no
> well-defined limit. That doesn't change the fact that each and every
> term is still finite.
Anyhow: Analysis and set theory supply different limits, namely a
limit larger than 1 and a limit less than 1. That's the point.
Regards, WM
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