Whatever method you use to generate your decimals, you can just slap an integer on each step of the way. You'll never run out of integers.
I'll put Cantor and his proof in a box, tell him to give me his fancy decimals quick as he can, and I can match each one with an integer no problem.
And pairing one infinite list with another infinite list doesn't make either one any more countable, because however high you count, they keep on going.
Whatever method you use to generate your decimals, you can just slap an integer on each step of the way. You'll never run out of integers.
I'll put Cantor and his proof in a box, tell him to give me his fancy decimals quick as he can, and I can match each one with an integer no problem.
And pairing one infinite list with another infinite list doesn't make either one any more countable, because however high you count, they keep on going.