The null space in an eigenvector function can be summed in linear systems, by linear algebra. - is proof of this.
I am only showing it this way, so as to desribe the irresistible truth in Plato’s Meno-s slave,as a way to reach the anti derivative. Kind of like showing the wisdom of zeno’s Paradox, and it’ solution being solvable backwards.
Plato, it seems left it to the future to come up with an explanation of this idea, or of ideas in general.
A “converging series” specifies a LIMIT for a summation. The LIMIT is equal to xxx. You can have two obviously different summation series with the same limit. Note that the summation must REACH INFINITY before it can equal its limit. And there is no “at infinity” to be reached.
And even a higher truth is that even if the summation could actually reach infinity, it still would not equal its limit because its definition forbids it from EVER summing up the last tiny bit.
That is irrelevant and Zeno’s can be solved easier than that via relative infinitesimals, “calculus”.
That is what must happen in order to make 1.0 = 0.999…, but the problem is that such can never happen.
Strange! Before James and I posted one could read the following text below Jerkey’s last post, although he was the last one who posted (before James and me):
“Last edited by jerkey on Wed Jun 29, 2016 5:24 pm, edited 2 times in total.”
How is that posible? Is it a wonder?
I don’t see anything astrange aboutbit, but perhaps i am missing something.
But wait, it happened again
Yes. Therefore all this operations have to do with the infinitesimal calculus (inveted by Gottfried Wilhelm Leibniz). So James is right with his answer.
Did you just make 2 edits to that post??
Or perhaps it is that your continued posts are being counted as edits due to their rapidity.
Look at the time that is mentioned below Jerkey’s post:
“Last edited by jerkey on Wed Jun 29, 2016 5:24 pm, edited 2 times in total.”
You posted after it. Look at the time that is mentioned above your post:
“by James S Saint » Wed Jun 29, 2016 5:48 pm”.
Strange!
Yeah 24 minutes seems like a lot of settle time required by a server.
James, you’re treating an infinite string as though it’s just a really, really long finite string (thus leaving a “last little bit”, presumably after the “last digit” at the “end” of the “endless” string…). That isn’t true. A really, really long finite string has a last digit, an infinite string does not. A really,really long finite string would indeed leave a “last little bit” left over, but we aren’t talking about a really, really long finite string, we’re talking about an infinite string. That distinction is crucially important.
And it was about 5:30 pm when I read that Jerkey edited his post. 
I have never seen that on ILP before. 
In addition: the server does not “know” when the next poster is going to post.
The rule is that it is not possible to read that you edited your post when you did it before the next poster posted.
Realize that as they make machines more and more clever, machines begin to be able to do what humans would think impossible. 
So could not the two impossibilities somehow have some sort of congruence?
No. That is what YOU are doing when you claim that there is a 0 “at the end once it gets to infinity”.
I am saying that because there is no end, the 9s must still be going - ALWAYS (true by definition). And thus never, ever becoming the string of 0s required for “1.000…”.
What two?
I was expecting that,James let me go back and recite from Your responses. Get back in a second
In Your response ending in ‘that clould never happen’ -5 of Your responses back in the forum, and the one two back, ending with ‘impossible’ - referring to machine intelligence.
It could never happen - is equivocal to - impossible
As per patterns, congruence and possibility.
The claim is that there are two decimal expansions for the number 1: a 1 with an infinite string of 0s after the decimal, and 0 with an infinite string of 9s after the decimal. Both are equivalent decimal expansions for the same integer. So there is no requirement that the 9s morph into a string of 0s, the string of 9s itself is equal to 1.
Multiple forms of the same value are common in math: 1/2 = 2/4 = 3/6 = 0.5 = .4999…
Jerkey, he simply means that the equation of 1 = 0,999… does at last not absolutely work: although the difference of both numbers becomes smaller and smaller, they can’t become equal, because there remains always a rest, an infinite small rest but a rest. So this equation works mathematically, of course, but that does not mean that it also works logically, thus philosophically. It is a solution for mathematicians but not for philosophers. One can always say that there is a rest that denies the equation.
This also indicates that mathematics and philosophy are two different disciplines, and history has shown that they have to be different disciplines.
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