Originally Posted by
Bruno J. We have the identity
which shows that it's impossible for the sequence
to be eventually constantly equal to -1. If it is eventually constantly equal to 1, let
be the greatest integer such that
. Then by hypothesis
and then
, contradicting the choice of
.
nice!
just note that before choosing the greatest integer
with
you should mention that basically the set
is non-empty.
this, of course, is trivial in our case because
but it becomes absolutely non-trivial if we replace
with an arbitrary non-zero integer
finally the identity you used can be extended. in general we have:
You always have nice problems, NonCommLion.
thanks! i like my new user name: NCL! it could also stand for Normal CLosure!
Where do you get them from?
here and there!