Sequences and subsequences.

Carla1985

Member
I'm trying to find a sequence that has subsequences that converge to every integer. The question before that was the same but just for the positive integers, for which i gave {1,1,2,1,2,3...} but I'm struggling to include the negatives. Thanks

Fernando Revilla

Well-known member
MHB Math Helper
I'm trying to find a sequence that has subsequences that converge to every integer. The question before that was the same but just for the positive integers, for which i gave {1,1,2,1,2,3...} but I'm struggling to include the negatives. Thanks
Choose for example $$0,-1,0,1,-2,-1,0,1,2,-3,-2,-1,0,1,2,3,\ldots$$ and so on. Notice that every integer appears infinitely many times: we can choose a subsequence that converges to a given integer. Besides, that subsequence is constant.

Carla1985

Member
That's fab, thank you!