Hm if you write  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  and  theres nothing the symbols would tell you about result being  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 omegaomega you have to look at the definition of omega and the axioms that hold for addition of ordinal numbers    ezander