> > 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.