- #1
jem05
- 56
- 0
hello,
Im reading goldblatt's NSA book, and i just finished the first part.
i have what i think are some trivial questions:
1) I am just wondering if *N is countable.
2) are limited elements of *R real?
3) I am 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.
Im reading goldblatt's NSA book, and i just finished the first part.
i have what i think are some trivial questions:
1) I am just wondering if *N is countable.
2) are limited elements of *R real?
3) I am 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.