hello, Im reading goldblatt's NSA book, and i just finished the first part. i have what i think are some trivial questions: 1) im just wondering if *N is countable. 2) are limited elements of *R real? 3) im trying to prove that if x is infinitessimal then cos(x) -1 is infinitessimal. i thought i can *-transfer the statement: (\forall n \in N) (\exists \delta \in R+) (\forall x \in R) (|x| < \delta) -->(|cos(x)-1|< 1/n) i thought if x infinitessimal, then |x| , 1/n for any natural integer, and that makes it < \delta so it will satisfy the transfer of the statement, making |cos(x)-1|< 1/n fr all n in *N. is that valid? thank you in advance.