On May 4, 9:30 am, Dan <dan.ms.ch...@gmail.com> wrote: > > > Either they're both relevant to Cantor's argument, or they're both > > > irrelevant . > > > Cantor's argument is a single-eyed look into the infinite. > > Forall n : d_n =/= a_nn is considered important. > > Forall n : (d_n) is in the list, is not considered important. > > > Regards, WM > > Why should it be considered important under the definition of > equality? If they have at least one different digit , THEY'RE > DIFFERENT. > It's not the least important that an atom of Albert Einstein appears > in you .You couldn't be more different. > > Every finite digit appears in the list at least once , but NEVER DO > ALL OF THEM APPEAR AT ONCE , IN THE SAME NUMBER. > When you play the lottery, you can get 1 number right , most of the > time . Just because for every possible number, you get it right at > least once ,when playing many times, doesn't mean you win the lottery. > YOU NEED TO GET ALL OF THEM AT THE SAME TIME . All digits IN THE SAME > NUMBER . > > THIS IS REQUIRED TO DISPROVE CANTOR : > exists n , forall m , a_nm = d_m > > THERE EXISTS A NATURAL N , SUCH THAT FOR ALL M, THE M'TH DIGIT OF THE > N'TH IN THE LIST IS EQUAL TO THE M'TH DIGIT OF THE DIAGONAL . > > It's a statement of the form : > There EXISTS a car in stock, such that ALL it's components are > LAMBORGHINI components . > > forall m , exists n , a_nm = d_m > This is what you prove . > For any LAMBORGHINY COMPONENT , at least one car EXISTS in stock that > has that component . > > You don't have a 100% LAMBORGHINI car in your stock (list) , so you > can't match the offer of the ANTI-DIAGONAL. > But , being the Snake-Oil salesman that you are , when someone asks > you : > > Do you have a 100% LAMBORGHINI car in stock? > You say : No , but I have a car with LAMBORGHINI steering-wheel . > ( digit k) . > But does it have LAMBORGHINI interior? (digit m) > You say : No , but I have ANOTHER car with LAMBORGHINY interior. > (digit m) . > But does it have LAMBORGHINI engine? (digit n) ..... and so on . > > And you keep on slick-talking the customer because you're to callous > to admit your failure to produce a full digit list . > > And would you stop it with the countable language already? You think > you can reduce experience to language? That there's a fixed language > than can capture everything, and everything that's not countable > doesn't exist, because your puny delusions of the omniscience of > language? "in the beginning, there was the Word" is rubbish . Not > even God could make a world out of words . You can make a story out of > language, but not the experience of a story. Not life. All the words > in all the languages of the world would couldn't adequately capture > your stupidity. I count on things uncountable, that experience is > unique. That the experience of the fragrance of any one flower could > not be captured in a trillion words . > > I find again ,sadly , that in this one circumstance , what cannot be > said must be passed down in silence.
Heh, engineers. Will we be making something today?
Combinatorially enumerate all b-ary sequences of length n. Obviously any less than b^n many is not all of them. As b and n increase, b^n >> n^2. It's never a square except for b = n = 1, or 2. A diagonal: is of a square. For b = 1, as n->oo, that looks to fill a triangle of lattice points, of an octant of a point lattice. For b = oo, n = 1, a column of lattice points that never increases in width. As b and n increase, the table of the points goes from square to asymptote, in the ratio of its dimensions.
Then, with n no less than infinity, where for each 2 < n < oo a "diagonal" or line through lattice points through (x_i, y_i) as to a square doesn't intersect b^n - n many of the rows: how can its complement be different from them, without containing their elements?
Doesn't much matter if nobody uses transfinite cardinals for calculus or other applications anyways, with "modern" mathematics shoehorned into measure theory then being ignored. Of course combinatorics is of vital utility in the concrete.
Then, with regards to the quote of Fefermann and the Kanimori paper on the infinite as of finitist, formalist method: the infinite isn't required to do some mathematics. But, the infinite is _in_ mathematics, of the objects of the domain of discourse, of mathematics: the universe of which is infinite.
Ah, the universe. If there's a "Theory of Everything": there's just the one. If not: there's just the one.