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by powera 3385 days ago
Step 1 fails because there is no such number that is an infinite number of 1s. Only infinity has infinitely many digits.

Step 2 fails because you can't create a 1-1 correspondence between the real numbers between zero and one, and the integers. That is what you are trying to prove. I'm too tired to figure out if your proof is valid or not, but your conclusion is correct.