Eram semper recta explained on 8/29/2021 :
> On Sunday, 29 August 2021 at 10:12:02 UTC-4, markus...@gmail.com wrote:
>> söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
>>> On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
>>>> lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
>>>>> On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
>>>>>> lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
>>>>>>> On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
>>>>>>>> fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
>>>>>>>>> On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com
>>>>>>>>> wrote:
>>>>>>>>>> torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
>>>>>>>>>>> On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com
>>>>>>>>>>> wrote:
>>>>>>>>>>>> onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
>>>>>>>>>>>>> On Wednesday, 18 August 2021 at 10:53:34 UTC-4,
>>>>>>>>>>>>> markus...@gmail.com wrote:
>>>>>>>>>>>>>> onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper
>>>>>>>>>>>>>> recta:
>>>>>>>>>>>>>>> On Tuesday, 17 August 2021 at 19:28:57 UTC-4,
>>>>>>>>>>>>>>> markus...@gmail.com wrote:
>>>>>>>>>>>>>>>> tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper
>>>>>>>>>>>>>>>> recta:
>>>>>>>>>>>>>>>>> On Tuesday, 17 August 2021 at 03:35:11 UTC-4,
>>>>>>>>>>>>>>>>> zelos...@gmail.com wrote:
>>>>>>>>>>>>>>>>>>> It is a WELL-FORMED NAME, unlike the bullshit 0.333... no,
>>>>>>>>>>>>>>>>>>> it's name is Bob, we write it as 1/3 Well, if one builds
>>>>>>>>>>>>>>>>>>> on shit, the end result is always shit.
>>>>>>>>>>>>>>>>>> That is why everything you have is shit. But the cauchy
>>>>>>>>>>>>>>>>>> constructions are valid and works fine.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> You DO CARE!
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I do not
>>>>>>>>>>>>>>>>>>> You still obey S = Lim S.
>>>>>>>>>>>>>>>>>> nope, again S=(0,0.1,0.11,0.111,0.1111,...)
>>>>>>>>>>>>>>>>>> S=Lim S
>>>>>>>>>>>>>>>>>> Substitute
>>>>>>>>>>>>>>>>>> (0,0.1,0.11,0.111,0.1111,...)=Lim
>>>>>>>>>>>>>>>>>> (0,0.1,0.11,0.111,0.1111,...)
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Is pure nonsense.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> What we have is S=lim S_n
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> HUGE difference.
>>>>>>>>>>>>>>>>>>> Your student Markus Klyver recently admitted it - not that
>>>>>>>>>>>>>>>>>>> it matters much because he is a moron just like you.
>>>>>>>>>>>>>>>>>> He has admitted that S=lim S_n, not your shit.
>>>>>>>>>>>>>>>>> S = Lim S_n is EXACTLY what is meant by S = Lim S.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Crank: One who cannot be convinced in the face of
>>>>>>>>>>>>>>>>> overwhelming evidence.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Fits you and Klyver perfectly!
>>>>>>>>>>>>>>>>>>> Of course what Euler wrote is of importance. Didn't you
>>>>>>>>>>>>>>>>>>> just say "build on the same foundational ideas"? You
>>>>>>>>>>>>>>>>>>> pathetic, stupid crank! The ideas he wrote is what
>>>>>>>>>>>>>>>>>>> matters, if he miswrote somewhere is much less important.
>>>>>>>>>>>>>>>>>>> You mean what YOU think matters. Chuckle. That is what
>>>>>>>>>>>>>>>>>>> matters to the mathematical community, of which you are not
>>>>>>>>>>>>>>>>>>> part. See, no answer because you know I am right!!!
>>>>>>>>>>>>>>>>>> Ah so by not addressing most of the things I post to you,
>>>>>>>>>>>>>>>>>> you admit here that I am right then.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Or are you gonna do cherry picking/be a hypocrite and say it
>>>>>>>>>>>>>>>>>> is suddenly different for you?
>>>>>>>>>>>>>>>> Why do you like to omit the subscript?
>>>>>>>>>>>>>>>> S=lim S is bad notation since the right hand side depends on
>>>>>>>>>>>>>>>> n, whereas the left hand side has no dependence on n.
>>>>>>>>>>>>>>> The left hand side IS dependent on the right hand side. It is
>>>>>>>>>>>>>>> the LIMIT of the series S. The limit is very much dependent on
>>>>>>>>>>>>>>> n and also how it is realised in analysis.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The series IS its nth partial sum. Nothing else.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It's S=lim S_n.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Grow a brain, you idiot! Suddenly you're worried about
>>>>>>>>>>>>>>> notation? LMAO.
>>>>>>>>>>>>>> The limit of the series (which is a constant) is the series
>>>>>>>>>>>>>> itself, but that not how the series is defined.
>>>>>>>>>>>>> Not at all. That is how you would like it to be, but the reality
>>>>>>>>>>>>> is very different.
>>>>>>>>>>>>>
>>>>>>>>>>>>> A series is NOT an infinite sum.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The series is defined as the limit of the partial sums S_n.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hence S = lim_n S_n. Right. S = Lim S. No difference.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> S = lim_n S is trivially the since S does not depend on n.
>>>>>>>>>>>>> S very much depends on its partial sums defined by
>>>>>>>>>>>>> S(n)=(1/3)[1-10^(-n)].
>>>>>>>>>>>>>
>>>>>>>>>>>>> S is defined by its partial sums. There is no such thing as an
>>>>>>>>>>>>> infinite S or even a unique S.
>>>>>>>>>>>> S depends on its partial sums, but not on n.
>>>>>>>>>>> Not quite correct. S depends on its nth partial sum as defined by
>>>>>>>>>>> S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n
>>>>>>>>>>> too, because the limit is realised by considering what happens as n
>>>>>>>>>>> becomes very large.
>>>>>>>>>>>
>>>>>>>>>>> The limit is a very clear concept. S is not infinite and CANNOT be
>>>>>>>>>>> defined in ANY other way, except by its partial sums. If you think
>>>>>>>>>>> otherwise, then you would have to show me ALL of S. You can't.
>>>>>>>>>>>
>>>>>>>>>>> There is no S = S_inf. That's just nonsense.
>>>>>>>>>>>>
>>>>>>>>>>>> It is lim_n S_n = S.
>>>>>>>>>>> NO. Lim S is very well defined to be 1/3 in the case of 0.333...
>>>>>>>>>>>
>>>>>>>>>>> All you've had so far is hand waving and excuses which for the most
>>>>>>>>>>> part are not even relevant to the discussion. You are trying to
>>>>>>>>>>> distract from the main topic which is the FACT that Euler defined S
>>>>>>>>>>> = Lim S and moreover that it was a very big blunder!
>>>>>>>>>> S=lim_n S_n =1/3 Nope. S is a series. Lim_n S_n is the number 1/3.
>>>>>>>>>> Two totally different objects, therefore cannot be equal. =0.333...
>>>>>>>>>> if (S_n) is the sequence 0.3, 0.33, 0.333, ...
>>>>>>>>> Bullshit. S = 0.333.... Lim S = 1/3
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No contradictions here.
>>>>>>>>>
>>>>>>>>> Right, only your garbage.
>>>>>>>> S and lim_n S_n are the same object by definition.
>>>>>>> Changing your tune again?
>>>>>>>
>>>>>>> No. S and Lim_n S_n are two different things. Your ill-formed
>>>>>>> definitions (ala Euler S= Lim S) are irrelevant. LMAO.
>>>>>> They are exactly the same thing by definition.
>>>>>>
>>>>>> S := lim_n S_n.
>>>>> You just don' get it, do you? You cannot say that a <series> is equal to
>>>>> a <number> because they are two different objects. You're such a moron.
>>>> A series *is* a number,
>>> Nope. A series is not a number.
>>>
>>> "In mathematics, a series is, roughly speaking, a description of the
>>> operation of adding infinitely many quantities, one after the other, to a
>>> given starting quantity." - The wikipedia moronica
>>>
>>> In other words, it cannot ever be a number because "adding infinitely many
>>> quantities" is a dream, in other words a super task which is impossible.
>>> LMAO.
>>>
>>> Look idiot, Euler defined it this way S = Lim S:
>>>
>>> Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+...
>>> &c.
>>>
>>> Only the dumbest mainstream academics are still arguing.
>>>> or a function that gives numbers for every x.
>>> What?! LMAO.
>> A series is a number (or a function that gives numbers).
>
> No, idiot. NO.
>
>> For example, Taylor series takes real numbers x and gives out a real number.
>
> A Taylor series (which is hopelessly inferior to the Gabriel Polynomial)
> never produces anything but a rational number approximation.

Wrong, you are mistaking a value for its representation as a series.
The value is in the generator, not in the representation.