While the mathematical equivalency raises an interesting point, the empirical difference between having and not having the 0 in the A Number seems to me quite consequential. In practice, it boils down to entering an 8 digit A# on our forms vs. entering a 9 digit A#. And with all the A#s out there, my intuition tells me that there is a significant difference between, say, A 012345678 and A 12345678.