On Jan 10, 2:31 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 10 Jan., 12:11, Zuhair <zaljo...@gmail.com> wrote: > > > > The anti-diagonal up to digit n must have a double up to digit n. > > > Of course, because the list is defined as the list of ALL terminating > > decimal representations. That is correct and natural and Cantor's > > arguments Agrees with that completely. > > Can you quote the relevant paragraph? > > > > > > Result: The diagonal cannot be an entry of the list. > > > the list > > ONLY contains TERMINATING decimal representations, while the diagonal > > and the anti-diagonal are non terminating decimal representations > > I do not know what you worship . Every finite initial segment of the > anti-diagonal is an entry of the list. I do not know what else can > belong to the anti-diagonal. But certainly this additional thing > cannot be used to distinguish it from anything.
Oh, that's really hard. Look I'll try to explain to you what you are saying an how ridiculous it is.
First YOU said that the list is that of ALL Terminating decimal representations of reals in the interval [0,1]. I take that to mean all decimals of the form 0.d_1d_2...d_n for all n=1,2,3,.... right.
Now there can be NO and I stress it again NO anti-diagonal that have an n-size initial segment that differs from all n-sized entries in the list mentioned above, to claim that there can exist such anti-diagonal is simply NONSENSE! Can you just understand that.
Again I stress it so that you can HAMMER and DRILL it in YOUR brain again there is NO such anti-diagonal at all.
Actually to be even more explicit on this case there can be NO real number whatsoever that can have each n-initial segment of it being different from every n-sized entry of the above list. I hope you can get what I mean.
NOT only that, also there can be NO real number whatsoever that can have an n-initial segment of it that is different from EVERY n-sized entry of the list, this cannot be, for a simple reason that is that n- initial segment of that real would itself be a member of the list of all terminating decimal representations, so OBVIOUSLY not such real can exist. THAT is a TRIVIAL remark actually.
However what you are not realizing is that Cantor never said nor did any of his argument even pave the road towards suggesting such a NONSENSICAL claim. The problem is that YOU have misread what Cantor said and What his arguments is implying, YOU think that Cantor's argument proves the existence of some real (which is the diagonal or sometimes called the anti-diagonal) which has an n-initial segment of it being different from EVERY n-sized terminating decimal expansion, i.e. differing from every n-sized element of the list you've defined. Again I stress that this is just YOUR misinterpretation of Cantor's arguments, Cantor never claimed nor does any of his arguments leads to such NONSENICAL TRIVIALLY FALSE claim that EVERYONE who is sane would obviously reject.
Can you just understand what is written above.
Zuhair > > > of course the diagonal and the anti-diagonal cannot be > > different (at a finite position) from all entries of the list, because > > the list is of ALL finite initial segments of reals, Cantor agrees to > > that, > > Can you quote the paragraph where it does that? > > Regards, WM
I don't need to quote any such paragraphs because this is just ABC of logic, and definitely Cantor is aware of such Trivial issue, these trivialities are not mentioned in papers of that importance because they are minor details that are very well understood and so trivial to mention.
I really really don't know why you think that a man of Cantor's caliber and that THOUSANDS of mathematicians among which are some who are regarded as geniuses of all times would really miss such a trivial remark that a clever child perhaps even at primary level school can capture. Are you serious? or you are just wasting our time? I'm really beginning to question your intentions, I think you are just playing around nothing more nothing less, because really I can't believe that you think that such a famous argument that lived for around a century or more can suffer from such trivial nonsensical error.