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Topic: Finally the discussion is over: S = Lim S is a bad definition.
Replies: 14   Last Post: Oct 6, 2017 10:47 AM

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 Jan Burse Posts: 1,472 Registered: 4/12/05
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 3, 2017 6:30 PM

BTW: It took me 2 minutes to find a sequence notation
in the works of Euler, maybe further examples can
be found. I used this website:

In 1910 and 1913, Swedish Mathematician Gustav
Eneström completed a comprehensive survey of
Euler's works. He counted and enumerated 866
distinct works, including books, journal articles,
and some letters he deemed to be especially important.
Each of these was assigned a number, from E1 to
E866, which is now referred to as the "Eneström
number." Most historical scholars today use
Eneström numbers to identify Euler's
writings quickly."
http://eulerarchive.maa.org/index/enestrom.html

The sequence notation I found is not perfect,
since later in his paper he stops with his
mortality considerations at age=100.

But I guess everybody gets the idea...?!

j4n bur53 schrieb:
> Or if you use the new mongo lingo of bird brain
> John Gabriel, you can also call it "not determinable".
> doesn't matter how you call it, a sequence is not
> the same as a value, but Euler clearly didn't use
>
> sequence notation in his public tailored publication,
> he used the infinite sum notation, thats John Gabriels
> error, that he thinks the following is not a
> limit notation, but a sequence notation:
>
> a1 + a2 + a3 + ...
>
> Here you find a nice publication by Euler, where
> he indeed mentions a sequence, and he uses this notation:
>
> (1), (2), (3), ...
> E334 -- Recherches generales sur la mortalite et
> la multiplication du genre humain
> http://eulerarchive.maa.org//docs/originals/E334.pdf
>
> So the difference is that he uses a comma in the
> above, and not a summation sign. It is not the case
> that mathematicians only wrote up sequences after
> Euler, sequence notation existed already during times
>
> of Euler. And clearly there is no Euler blunder S=Lim S,
> this is complete bird bran John Gabriel nonsense,
> to denote a sequence, Euler would have used the comma.
> BTW in the same paper E334, you later find
>
> also sum instead of comma, so Euler was even able
> to use sequence and series side by side.
>
> Am Dienstag, 3. Oktober 2017 23:51:43 UTC+2 schrieb burs...@gmail.com:

>> limit, since {an} or (an) wants to
>> indicate a multiplicity of values, but

>
> John Gabriel schrieb:

>> Finally the discussion is over: S = Lim S is a bad definition.
>>
>>
>> Comments are unwelcome and will be ignored.
>>
>> Posted on this newsgroup in the interests of public education and to
>> eradicate ignorance and stupidity from mainstream mythmatics.
>>
>> gilstrang@gmail.com (MIT)
>> huizenga@psu.edu (HARVARD)
>> andersk@mit.edu (MIT)
>> david.ullrich@math.okstate.edu (David Ullrich)
>> djoyce@clarku.edu
>> markcc@gmail.com
>>

>

Date Subject Author
10/3/17 bursejan@gmail.com
10/3/17 bursejan@gmail.com
10/3/17 Jan Burse
10/3/17 Jan Burse
10/3/17 Jan Burse
10/3/17 Me
10/3/17 Jan Burse
10/3/17 Jan Burse
10/3/17 Jan Burse
10/3/17 Dan Christensen
10/3/17 zelos.malum@gmail.com
10/4/17 bursejan@gmail.com
10/6/17 genmailus@gmail.com
10/6/17 bursejan@gmail.com