# I got an email with this attached file

• Nymfa
In summary, a new member named Nymfa joined a forum and accidentally deleted their first post. They asked for help regarding an interesting attached file they received via email. Another user warned them about a person named Doron Shadmi, who is known to make elementary mistakes in their mathematical proofs. Nymfa asked for a professional opinion on the file and another user pointed out a mistake in the proof. Nymfa defended the file, stating that it presents a non-common point of view on convergence of sequences. However, another user explained that the non-common point of view is incorrect and that there cannot be any interval between all the points in a convergent sequence and the limit point. Nymfa continued to defend the file, arguing
Nymfa
Hi,

I am new here and this is the first time for me to use this kind of a forum
and I think that I delete by mistake my first post so here it is again.

I am a russin student and I got an email with this attached file (I got newer version of it yesterday).

It looks very interesting but I need to know more details about it.

Can someone here help me?

Thank you.

Nymfa

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He is a complete crackpot who was a major nuisance at PF earlier.

Hallo arildno,

I do not know about Doron Shadmi and I do not care.

All I care is what I read and it looks interesting.

Thank you.

Nymfa

Step 4 is wrong; pick a sequence of increasing irrationals converging to "r".
If there existed a "q" less than "r" so that "q" was bigger than any of the irrationals in the sequence, then the sequence would always be a greater distance than r-q from r.
But this contradicts convergence of the sequence.

Yes I have noticed that, but the interesting part of this paper is in the dialog,
where we can see that this person is aware about the convergence of the sequence, but gives a new expalanation, which put Cantor's diagonal in a new light.

Nymfa

The dialog at the end is the typical gibberish Doron Shadmi loves to indulge in.
Without fail, once he tries to show how his ideas supposedly apply to real maths, he stumbles, and makes elementary mistakes as the one I mentioned above.

That is what you should judge him by, not his vague, private language as given in the dialog.
Wrong is wrong; his "proof" doesn't hold together, and his dialogs are irrelevant in this context.

Maybe this is not the common point of view about convergence of a sequence, but I do not see (yet) any problem in this non-common point of view.

Can you find some problem in this non-common point of view?

Nymfa

Possibly others at PF will go through the dialog in detail, I won't, since I am sick and tired of Doron Shadmi.

However, read again person "a"'s very first comment:
Here, that person has a totally wrong conception of what it means that there are "more" irrationals than rationals, in that he thinks that irrationals must always lie closer to any particular number than the rationals do.
But, since to any real number "b" we may find a sequence of composed of rational numbers converging to that number (without "b" being in that sequence), there cannot exist an irrational number "i" strictly between "b" and all the rationals in our sequence.
Thus person "a"'s first comment is totally meaningless.

Possibly, someone else here might want to tackle the rest of the dialog; I won't.

But, since to any real number "b" we may find a sequence of composed of rational numbers converging to that number (without "b" being in that sequence), there cannot exist an irrational number "i" strictly between "b" and all the rationals in our sequence.
Thus person "a"'s first comment is totally meaningless.
But do not forget that we are talking about the real-line, where rational and irrational numbers are mixed with each other, so in this case, since (by the common point of view) there are more irrationals than rationals, we can find more irrational numbers in x-q interval where x can be rational or irrational number. so I think Doron is right here, unless you can show a rigorous proof, that clearly show that there cannot be any irrational number in the domain of x-q, where x is a rational number.

Nymfa.

There simply isn't any interval lying in-between between all the points in a convergent sequence and the limit point of that sequence.

But we have here two disjiont sets, where the limit point (limit number x) is in a one set and all the other numbers (which non of tham is x) are in another set.

Since the real-line has the power of the continuum, there must be some element that coleses the gap between these disjoint sets.

Nymfa

Nymfa said:
But we have here two disjiont sets, where the limit point (limit number x) is in a one set and all the other numbers (which non of tham is x) are in another set.

Since the real-line has the power of the continuum, there must be some element that coleses the gap between these disjoint sets.

Nymfa
No, Doron; you're wrong. Yet again..

Not Doron, Nymfa,

So where is the rigorous proof that Doran is wrong.

For example: the limit number is {pi} where any number within L (which is the set of all irrational numbers that are smaller than pi) is not pi.

In this case there is always an unclosed gap between set L and the singleton set {pi}, but since we are talking about the power of the continuum, only a rational number can close this gap and save the continuum.

No, Doron. I have already given you enough rigour.
The fact that you are unable to grasp this, and remains trapped in the mental muck you've buried yourself in, isn't my fault.

arildno call me whatever you like, but also give here a rigorous proof about the augment in my previous post.

There is some very fundamental notion here that no proof can contradict, if a set is a collection of infinitely many elements, where each element can be clearly distinguished from the other members, which share with it the same set.

There is inseparable connection between identification and belonging which is essential to our ability to define sets, especially if a set is determined by the identity of its members (or their absence in the case of the empty set).

Anything which is not x can be smaller or greater than x, and this is an essential state that cannot be breaked down by a logical system, which is based on the belonging concept that is based on the identity of the belonged elements.

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If you aren't Doron, then you are probably a rational person capable of seeing the egregious errors in anything Doron writes. Arildno has explained some to you, that you are incapable or unwilling to understand them is not his fault. Anyone can see that Doron knows nothing about maths, and we can safely dismiss him as a crackpot. It's just a shame he keeps inventing pseudonyms and trying to foist his garbage on others. So, if you aren't he then simply stop encouraging him. If you are he, and last time Doron posted under a pseudonym he complained about the accusations as well, then please for the love of whatever God you may believe in, or just humanity, please leave us alone.

Actually, your syntax and phrasing means you are Doron. No one else quite writes like that: references to "based on", "belonging", "ability", "fundamental notion", "distinguished". And it takes no one of any great intellect to see that you stopped presenting this as a curio sent to you, and made it clear this was your theory.

Look, I am Russian student and many students in our class think that the attached paper in my first post is an interesting work.

For the past two weeks we discussed about this work in our class, and when we showed it to our professors they reacted like you, without giving any rigorous proofs to our claims.

I think that something is wrong here because no one of our professors and (yet) no one of you in this forum really gave a rigorous logical proof, that clearly shows that this work fails.

Then many students in your class are complete fools. As I know lots of Russian educated mathematicians, I know that generally they are actually far more educated than other nationalities of students, so I don't believe for one second that there is a class of them who thinks anything written by Doron is remotely interesting or sound.

Tell you what, why don't you define all of the terms in that pdf that are not part of any rigorous mathematical framework, to use a Doronism. Though I wouldn't bother posting youe definitions here cos no one will be bothered with them.

Please, check out the history of this crank, crackpot and general ignoramus.

Then many students in your class are complete fools.
I am going to show it two my class.

We have decided that we are going to send this work to other students around the world. We did it, and today we know of about more than 100 students that have this work and no one of them got until now any rigorous proof that shows that this work fails.

You should also show them the bit where I say that I think Russian educated mathematicians aren't fools, then, and thus that you are Doron, right down to his syntax, grammar, and style.

This is my last post in this forum.

I put it in a word file and I will show it to my class at monday.

If you have a rigorous proof to show that the work at the first post failes, then write it down here.

I can't quite believe that I'm doing this, but let's play the game for one post:

Surely any Russian mathematician would notice that point 4 of page 2 contains a conclusion that is ridiculous, since Sup(L) =r, which is irrational, though you/he states it is rational. Of course if you are saying you don't know what a Sup is then that only adds to the mystery of claiming to be a Russian student (you misspelled russian, by the way in the first post). Unless you're a Russian student of something other than Maths, that is.

The sentence immediately after statement 4 is utter tripe and doesn't make sense in English, never mind mathematics.

The dialog's first exchange indicates that Doron is completely unaware that the denseness of Q or the irrationals in R is not a statement about their cardinality, and in fact that he is a crank who can't be bothered to learn the definitions.

It is, in short, utter crap that doesn't make any sense. It's a little hard to explain in "rigorous" terms why it is not correct, since the answer is "it's meaningless strings of symbols". Why don't you try explaining why it is correct?

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