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**Philosophy, Religion & Society / Number that cannot be written**

« **on:**January 31, 2008, 04:01:27 PM »

I dont know if im gonna do this one justice or not, but its an interesting paradox. Im saying its philosophy because it sure aint any of the others.

Ok, so. You take every number between 0 and 1 (an infinite ammount)

You the lengthen them to an infinite length by adding 0s on the end

so 0.1 becomes 0.1000000000000000(etc)

then, you take the first digit of the first number, and the second digit of the second number, and the nth digit of the nth number and so on. and you call that number X

then you take number X, and write it out again, but you add 1 to all of the digits (9 looping round to 0). call this number Y

This number has to be different to all the other numbers in the list, as X contained one digit from every digit in the list and number Y has every digit different to the one in number X.

Hense, we have not written number Y in the list, even though it contains every number between 0 and 1.

Ok, so. You take every number between 0 and 1 (an infinite ammount)

You the lengthen them to an infinite length by adding 0s on the end

so 0.1 becomes 0.1000000000000000(etc)

then, you take the first digit of the first number, and the second digit of the second number, and the nth digit of the nth number and so on. and you call that number X

then you take number X, and write it out again, but you add 1 to all of the digits (9 looping round to 0). call this number Y

This number has to be different to all the other numbers in the list, as X contained one digit from every digit in the list and number Y has every digit different to the one in number X.

Hense, we have not written number Y in the list, even though it contains every number between 0 and 1.