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This question already has an answer here:

Is there any totally ordered field with cardinality larger than the continuum? If such field exist, please give an example (an simple one if possible).

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marked as duplicate by user642796 Dec 2 '15 at 11:28

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    $\begingroup$ The surreal numbers are an ordered field that is a proper class, so it’s too big even to have a cardinality. $\endgroup$ – Brian M. Scott Dec 2 '15 at 11:28
  • $\begingroup$ re Brian M. Scott: What if I also require it to be a set? $\endgroup$ – A. Chu Dec 2 '15 at 11:43
  • $\begingroup$ See the earlier question. $\endgroup$ – Brian M. Scott Dec 2 '15 at 11:45