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, or a function that gives numbers for every x.