How to prove that the sum of the digits of two natural numbers must be greater than the sum of the digits of the number equal to the sum of two natural numbers?

How to prove that the sum of the digits of two natural numbers must be greater than the sum of the digits of the number equal to the sum of two natural numbers?


There is a problem in the proof of mathematical induction! His proof is that the sum of the digits of 1 + 1 = 2 is equal to the sum of the natural digits. Then according to his theory, the two digits can be proved to be equal forever! In fact, it is very simple. If the addition of two natural numbers does not produce carry, it must be each number