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Sequences and subsequences.

Carla1985

Member
Feb 14, 2013
93
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
Jan 29, 2012
661
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
Feb 14, 2013
93
That's fab, thank you! :)