Prove the following

Consider the following criteria for integers:
- The digits in the number are sorted(ascending order, left to right)
- The digits in the square of the number are also sorted
(Ex: N=12 N^2 = 144 fits the bill, but N=11, N^2 = 121 - does not. )

Prove that the number of numbers that satisfy this criteria is infinite.
(Got it from Knuth's lectures on the Stanford site.)