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There is no transfer principle in the surreals other than the one transfered from the hyperreals. Therefore it one wishes to do analysis with anything smaller than the absolutely largest class of numbers, the surreals are not an option. For example, all real functions extend to the hyperreals, but even such a simple function as the sine does not extend to the surreals (without passing via an identification of a maximal class-size surreal field and exploiting an identification of the latter with a class-size hyperreal field and importing a hyperreal transfer principle via the identification).