 Hm, if you write '2+3=5' are you then 'calculating by the visual characteristic of the numbers?' I think not. If you wrote 'II + III = IIIII' then yes, but if you add 2 and 3 there's nothing the symbols would tell you about result being 5 (you have to go back to the definition of the symbols and the Peano axioms to get this result). And exactly the same holds here. If you want to add 'omega+omega' you have to look at the definition of omega and the axioms that hold for addition of ordinal numbers.    (ezander)  