On 26 Okt., 23:03, "Dirk Van de moortel" <dirkvandemoor...@nospAm.hotmail.com> wrote: > WM <mueck...@rz.fh-augsburg.de> wrote in message > > a9060de6-33f1-45ba-ac0a-0dfef22e2...@s7g2000yqa.googlegroups.com > > > On 26 Okt., 21:33, "Dirk Van de moortel" > > <dirkvandemoor...@nospAm.hotmail.com> wrote: > > > > We can easily define and verify statements like > > > Limit( x --> +infinity; ( f(x), g(x) ) = ( +inf, 0 ) > > > > Can you do a similar thing with your SetLimits? > > There were four
Sorry, I read three questions only, namely definitions and proofs for the limits |N, { } and the last sequence of pairs.
> questions preceding this one: > > S_n = { 1 , ... , n } > Can you formally *define* a SetLimit and then prove that statement > SetLimit( n --> +inf, S_n ) = |N > ?
done > > and > > T_n = { 1/2 (n-1) n + 1 , ... , 1/2 (n-1) (n+2) + 1 } > Again, can you formally *define* a SetLimit and then prove that statement > SetLimit( n --> +inf, T_n ) = { } > ?
done > > You have answered only two of them. > Can you *prove* them formally?
Of course, but you should be able to do that by yourself, after knowing the definitions. Therefore I will give only an example how you should proceed:
