Question about Cantor diagonalization

To keep it short, the question is: why as I add another binary by Cantor diagonalization I can not add a natural to which it corresponds, since Natural numbers are infinite?

Is it not implying Natural numbers are finite?

To keep it short, the question is: why as I add another binary by Cantor diagonalization I can not add a natural to which it corresponds, since Natural numbers are infinite?

Is it not implying Natural numbers are finite?