Take the 2-minute tour ×  What is the cardinality of the set of
hyperreal numbers?  share|improve this question What do you
think it is? Also, you could have checked on Wikipedia before
asking here. –  t.b. Jul 27 '11 at 12:43 Your question literally
asks about the cardinality of hyperreal numbers themselves
(presumably in their construction as equivalence classes of
sequences of reals). You probably intended to ask about the
cardinality of the set of hyperreal numbers instead? –  joriki
Jul 27 '11 at 12:49 @joriki: Either way all sets involved are of
the same cardinality: $2^\aleph_0$. –  Asaf Karagila Jul 27 '11
at 13:02 Yes, I was asking about the cardinality of the set oh
hyperreal numbers. Thank you. –  zar Jul 27 '11 at 16:50 add
comment  1 Answer  up vote 13 down vote accepted  The Hyperreal
numbers can be constructed as an ultrapower of the real numbers,
over a countable index set. I will assume this construction in
my answer.  The hyperreal field $^*\mathbb R$ is defined as
$\displaystyle(\prod_{n\in