I think you are extremely confused. Digits and rows of WHAT? Cantor's proof is a proof by contradiction: You ASSUME that there are as many real numbers as there are digits in a single real number, and then you show that that leads to a contradiction. You want a proof of something that Cantor proves was false.
You know very well what digits and rows. The diagonal uses it for goodness' sake. Please stop this nonsense.
When you ASSUME that there are as many real numbers as there are digits in a single real number, this isn't true for N either. It's a given that it isn't true. If it's not true for N, what does it matter that it's not true for R?