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Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. However I have been able to visually disprove Cantor's Diagonal argument simply by reordering the sequence .. like such below... As you can clearly see, in such a sequence every Natural number is listed (& in order) and will eventually get enumerated, corresponding one-to-one to all natural numbers. By listing it this way, I can now show that I can draw a diagonal slash from upper left corner to the lower right corner and this slash contains a infinite number of "0".. X= 000000000000.... Therefore it goes to show and follows from the above that by changing "any" and "every" nth digit of X I am able to make it "fit" any of the horizontal sequence of elements!!! In general, for since I am able to order it in such a way that I can show that the progression of the natural numbers is "slow" enough that it never has a chance to catch up to the "diagonal", then effective at each and every sequence level "X" can be manipulated to be exactly that sequence! Therefore Cantor's Diagonal Slash has been disproved. Happy Halloween update: for further clarification look at this new graph I posted.. Essentially for / at every nth digit level of X, (say if X is only 2 digits) there is NO possible combination of X that anyone could possibly come up with that isn't contained in the sequences demarcated by the red rectangle, same is true for when x is at three digits, four digits, for any number of digits of X (indeed for any value, discrete or 'real') of X, there is already EVERY possible combination of that X enumerated one by one according to the natural numbers already belonging in that list! As you can see, it is not possible to come up with any sequence of numbers no matter how "picky" you are that isn't already in the list! Therefore again Cantor's Diagonal Slash is disproved.

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