Post by bassam karzeddinOK, I will retake the pain to repeat the hidden themes in my reasoning to all of my previous seemingly ridiculous claims and without offering you the earlier standing old challenges that I did claim
And let me assume in good faith (despite you are anonymous) that you are very serious and true fact searcher but very clueless and rarely educated about my posts, assuming also that you have the minimum elementary education in number theory and geometry (which is most mathematics about)
And kindly follow the steps in the hope that a sparkling idea might get deep into your own thinking to restart considering maths from its start
And of course, this is only one of many elementary ways to start rediscovering what is the true math and what is the bad math
We have this simple ***UNSOLVABLE*** Diaphontine equation,
[A(n)]^2 = 2*[10^n]^2 ,.... (1)
Where (n) is a natural number and A(n) is natural number say here in base 10, but with (n + 1) digits and
And as mentioned above, there are no existing natural numbers like (n, A(n)) that can ever satisfy Eqn. (1), since that was proved rigorously by the Greeks and in half a page or so and since few thousands of years back
Proof completed, Right? Please object immensely if you don't agree
You prove that the square root of 2 is not a rational number of the exact form A(n)/10^n. No one should be surprised by this or reject this. (There is the possibility that because of your history some might reject anything you might claim, but that is a much larger issue to deal with)
Post by bassam karzeddinThen, what about a so innocent academic professional mathematicians who simply didn't notice this unsolvability and wrongly thought that if we divide Eqn. (1) by (10^n), where it becomes like this
I do not believe that anyone did not notice this or that anyone believed that sqrt(2) == A(n)/10^n is an exact decimal form. If you claim that any careful academic did not notice this then please present documentation showing where they missed this. Raging arguments in sci.math almost certainly do not count. Far too much silliness is here for this to count.
Post by bassam karzeddin2 = [A(n)/10^n]^2, ... (2), AND further assumed (x = A(n)/10^n), where we have (2 = x^2), and taking the absolute value os square root of both sides you get
Sqrt(2) = A(n)/10^n, where n tends to (but never equal) to no number like infinity
So, you have your true irrational number (as distance diagonal of a square with arbitrary existing distance side as unity, and based solely on the Pythagorean theorem and nothing else, being expressed approximated in rational decimal from saying base 10 for simplicity, as below
I do not understand where absolute value came from, but that does not seem essential.
Approximation is not the issue, that appears to be only a distraction. You are dealing with exact numbers.
Post by bassam karzeddinFor (n = 1), A(n) = 14, and first approximation FOR sqer(2) becomes as (14/10 = 1.4), similarly for (n = 2), the seconed approximation becomes
like A(2)/10^2 = 141/100 = 1.41, ..., AND for (n = 10), you have
A(10)/10^10 = 14142135623/10^10 = 1.4142135623
1) *Please note that the decimal notation isn't any magical tool but basically a division notation operation, Right?
2) Also, note that the word "TENDS TO" doesn't strictly mean "equal to" or "greater than" but certainly "Less than", but how less than infinity one can truly go? (ask your self first)
And make sure that when you tend to your no number "infinity" that you are always nearer to "ONE" than that "INFINITY" only in your mind, Right? Wonders
Otherwise, your sqrt(2) would become ultimately like a ratio of two nonexisting natural numbers like this
A(n-->00)/10^{n-->00) = 14142135623.../10000000000...
= No-number/ No number = No number
But one usually gets normally deceived when writing it the same thing with a decimal notation like this
(sqrt(2) = 1.4142135623...) and be happy also!!
But that (14142135623...) isn't any existing number since No (n, A(n)) never exist from that proved Diaophontine equation above, Right?
So, you have a true existing number like sqrt(2) but with no decimal form equivalence but only ***PERPETUAL***APPROXIMATIONS***, Hence
Sqrt(2) =/= 14142135623..., (prof finished)
If you say there is no FINITE decimal equivalence
Sqrt(2) =/= 1414
or
Sqrt(2) =/= 1414135
then I believe everyone would agree with you. You can go places which have not seen your history of claims and ask if they agree that there is no finite decimal which is exactly the square root of 2 and everyone should instantly agree with you.
But if you instead go to those same places and ask if
Sqrt(2) =/= any infinite stream of decimals
Then I think that no one will agree with you and you are going to need far far more powerful and convincing proofs if you ever expect to convince anyone else of this.
Post by bassam karzeddinAnd in very similar analysis no number ever exists when those three meaningless dots (...) added to it on the wright side
Ah, the infinite behaves very differently from the finite. You believe the dots are meaningless, but only to you. To everyone else the dots have well understood meaning.
Post by bassam karzeddinCouldn't you too see yet the very thin line between a shining bitter fact and a very sweet business human mind fallacy? wonders!
It seems to me that the difference between finite and infinite is much more than a very thin line. The difference is larger than we might imagine.
But let me ask one question before we go on. Perhaps this is not your point of this particular proof, but I want to make certain I understand.
You want to distinguish between the constructible and the non constructible. That seems essential to your thinking. You believe the non constructible are completely different, in fact they do not exist.
Suppose you repeat carefully step by step your above argument using the cube root of 2 instead of the square root of 2. And thus you use cube instead of square.
Since you claim the cube root of 2 does not exist I would think that there should be some fundamental obvious difference at the end of that process. But I do not see any difference. Both square root and cube root are not rational. Both do not have any finite decimal result. Why is there no difference between square root of 2 which is constructible and cube root of 2 which is not constructible?
Post by bassam karzeddinOr must that be repeated indefinitely for day and night and forever to understand?
If you are claiming there is no finite decimal number for the square root of 2 then I don't think you need to do that even once. I don't think anyone should claim there is a finite decimal value for square root of 2.
If you are claiming there is no infinite decimal number for the square root of 2 then I think you will have to find much more convincing arguments to get anyone else to ever believe you.
A larger claim is that there is no finite decimal number for any constructible irrational number. Everyone would believe that even without your proof.
There are even easier numbers with no finite decimal number. 1/3 or 1/7.
Before we go any further and to any greater questions. What does this proof give you? It does not seem to distinguish constructible from non constructible. It does not distinguish rationals with no finite decimal form from non constructible. All it seems to do is distinguish rationals with a finite decimal form from numbers, constructible or not, without a finite decimal form.
I am only guessing that you want this proof to give you some evidence against decimals, perhaps against all decimals. But it only seems to distinguish between 3 and 1/2 and others with finite decimal form versus 1/3 and 1/7 and square root of 2 and cube root of 2 without finite decimal form.
Unless you have some much more powerful result that I do not see in dividing numbers into these two groups then I do not see what this has accomplished.
Post by bassam karzeddinHowever, this only one of a dozen of more simpler proofs and not only by myself but with many revolutionary independent thinkers like (JG, WM, Kong Dong, AP, David, ...) with some different points of views, who usually described as CRANKS by the vast majorities of Anonymus academic mainstream professional mathematicians and alike
I try to focus on ONE proof at a time. Other proofs written other times and many times, I try to focus on one concrete thing at a time and not make mistakes.
Post by bassam karzeddinI'm afraid that you didn't learn anything useful yet from this very elementary lesson
I learn you prove square root of 2 =/= A(n)/10^n is not a rational number. That is not surprising. Everyone agrees with that. And there is no finite decimal number which is square root of 2. That is not surprising. Everyone agrees with that. And you do not believe in ... or infinite decimals. No one else agrees with that.
If I am supposed to have learned something more than that then please very clearly state what that is.
Post by bassam karzeddinAnd if unexpectedly yes, then prove that nither (pi) nor 2^{1/3} are truly any real existing numbers but solely a human-invented like numbers that never existed as exact distances relative to any existing unity distance
Yes. Finally you bring in constructible at your conclusion.
Because you do not believe in infinite decimals you do not seem to believe in any number which is an infinite decimal. These include 1/3 and 1/7 and square root of 2 and pi and cube root of 2 because all those are infinite decimals. But 1/3 and 1/7 and square root of 2 exist as exact constructible distances relative to existing unity distance.
It seems that
You believe only constructible numbers exist. Fine. Begin each of your posts, as I have suggested several times, with "Suppose only numbers which can be constructed with compass and unmarked straight edge exist." Any reader should look at that and expect to work in that domain. But for some reason you desperately do not want to do that.
But what then happens if someone changes "compass and unmarked straight edge" to slightly different tools. Then a different domain exists. You may have to start at the beginning and prove everything about that domain before readers will trust it. If you put one mark on the straight edge then a whole different world of numbers are created. Or if you replace the straight edge with another instrument then another different world of numbers are created.
You do not believe infinite decimals exist. Fine. Then you have to deal with 1/3 and 1/7 and square root of 2 and cube root of 2. Begin each of your posts with "Suppose only numbers with finite decimal values exist." That is an even more restricted domain and not commonly used. You may have to start at the beginning and prove everything about that domain before readers will trust it.
It appears that you are trying to create a world that you can take credit for and is all your own. But rational versus rational+irrational does not seem enough. But finite versus infinite decimal does not seem enough. But constructible versus non constructible does not seem enough. I think you need to find some tool, some basis that everyone else already understands and accepts and that tool or basis is exactly precisely enough to divide the world where everyone else lives from the world where you want to live. I do not believe you have found that tool yet.
I do not think finite versus infinite decimals is going to get you what you need. That does not seem powerful enough to distinguish 1/7 from cube root of 2. So you might consider giving up on your infinite decimals and look for something more precise and powerful.
I do not think constructible versus non constructible is going to get you what you need. I think you need something more powerful and precise than that.
Post by bassam karzeddinGood luck
Bassam King Karzeddin
Please make your claims more precise and powerful and eliminate everything that is not absolutely essential to a single specific result.
I think you can condense your post to something much simpler. Ask yourself if every reasonable mathematician believes a claim. If so then you need not even mention it or anything about it. But if not a single other person in the world but you believes a claim then you are going to need an astonishingly powerful correct convincing proof of that claim and nothing else.
Good luck
qbwr