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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.

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# Non-Standard Analysis

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