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Good questions. I don't know enough about hyperr. numbers to say if they can be embedded into the surr. numbers. Studying they hyperreals is still somewhere on my to-do list. There are some very nice resources on Hyperreals and non-standard analysis on-line: |
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Good questions. I don't know enough about hyperreal numbers to say if they can be embedded into the surreal numbers. Studying they hyperreals is still somewhere on my to-do list. There are some very nice resources on Hyperreals and non-standard analysis on-line: |
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The URL http://www.tondering.dk/claus/surreal.html for the "gentle yet thorough introduction" doesn't (currently) seem to work, nor does any obvious modification of it. As for the non-commutativity of ordinal addition, sure, but there is something called the "natural" or "Hessenberg" sum on ordinals which is commutative. (The definition uses the Cantor normal form, and basically just "sorts" the summands.) Maybe this is what extends to Conway's addition? |
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