Wednesday, February 16, 2005

Infinite Binary Table Paradox

Listen to this...
Take a table, with an infinite ammount of rows. Each row is a string of binary digits (0's and 1's). Now, each row is infinitely long, and there are an infinite ammount of rows, this is ok because there are an infinite ammount of possible combinations if we have an infinite length for each row.
But, now we create a new row, call it n, made up of the first number from row 1, the second from row 2, etc. but inverted. So, row 1 starts with a 0, so we place 1 in position 1 of row n. This means that n cannot be in the infinite ammount of rows, because each place in n is copied from another row, but inverted so it cannot match any one row. Therefore we have an infinite ammount of rows, containing all possible combinations, but it cannot contain row n. Weird.

1:010101010
2:001010110
3:110101010
4:101010111
5:101011111
n:11110...........

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