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statdad

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Partially true. Remember, you made the list by assuming the numbers between 0 and 1 form a countable set, so can be placed in order from smallest to largest, and so your list already contains all of those numbers.

Now, when you go down the diagonal to create the new number, the procedure discussed does not stop at any particular row (say the 500th). Instead, it shows you can go down all rows, creating a number that is different from EVERY other number in your (assumed to be complete) list. So now you have this:

* You assumed you could list every possible number, and that you have done so

* You find out your assumption was wrong

That is the key to the argument.

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