[HN Gopher] The wonderful world of Surreal numbers
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       The wonderful world of Surreal numbers
        
       Author : signa11
       Score  : 28 points
       Date   : 2021-06-26 11:30 UTC (1 days ago)
        
 (HTM) web link (ianopolous.peergos.me)
 (TXT) w3m dump (ianopolous.peergos.me)
        
       | skissane wrote:
       | > all the different infinities
       | 
       | Is this true? They talk about surreals defined on day aleph-null.
       | Is there a day for every possible cardinal? What about large
       | cardinals?
       | 
       | https://en.wikipedia.org/wiki/List_of_large_cardinal_propert...
        
         | gjm11 wrote:
         | Yes, it's true.
         | 
         | Each ordinal appears at the day with its number; e.g., omega
         | (first infinite ordinal, kinda corresponds to aleph-zero)
         | appears on day omega, 2^omega appears on day 2^omega, etc.,
         | etc. There is a day for each _ordinal_.
         | 
         | There are whatever large cardinals the underlying set theory
         | has. (Though Conway took the view that rather than building the
         | apparatus of surreal numbers on top of a particular set theory
         | like ZFC, you should think of this as its own theory that
         | resembles set theory but has two different kinds of "set
         | membership" (left and right) and someone should prove a theorem
         | saying that such things are always at least as consistent as
         | ZFC...)
         | 
         | I don't think large cardinals play any particular role in the
         | theory of surreal numbers, games, etc.
        
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