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By my understanding, to define denseness the field needs to be ordered otherwise you can't say A<B<C. I get the vague feeling all ordered fields are dense, but that's by assuming the two field operations are always addition and multiplication, since they allow you to always generate 0.5(A+B) from A and B and by ordering A<B => A<0.5(A+B)<B.

Usually when I attempt such general lines of logic I go horrifically wrong, so are there ordered fields which aren't dense? The list of ordered field Wiki gives doesn't have any which immediately jump out as non-dense, but some I'm not exactly familiar with.

Thanks