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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: 1,457 Registered: 4/12/05
Re: Finally the discussion is over: S = Lim S is a bad definition.
Posted: Oct 3, 2017 6:41 PM

One more example, comma, on the first page:
http://eulerarchive.maa.org//docs/originals/E449.pdf

j4n bur53 schrieb:
> 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