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Nov 20, 2023 at 11:36 comment added Ville Salo For Banach density 1, you can just observe that there are arbitrarily long intervals there, taking the $k_i$ to form an interval.
Nov 20, 2023 at 11:30 history edited HumbleStudent CC BY-SA 4.0
added 40 characters in body; added 31 characters in body
Nov 20, 2023 at 11:28 comment added HumbleStudent What about Banach density? I will also include that in the question as you reminded me.
Nov 20, 2023 at 11:26 comment added Ville Salo For natural density it is false. Consider any set whose prefixes are Følner in the sense that the set is eventually built from longer and longer intervals. Then your intersections don't change density.
Nov 20, 2023 at 11:18 comment added Ville Salo Which type of density?
Nov 20, 2023 at 11:07 history edited gmvh CC BY-SA 4.0
Improved grammar and punctuation
Nov 20, 2023 at 11:01 history edited YCor CC BY-SA 4.0
edited tags, emphasized the statement and that OP not certain about it
S Nov 20, 2023 at 11:00 review First questions
Nov 20, 2023 at 11:07
S Nov 20, 2023 at 11:00 history asked HumbleStudent CC BY-SA 4.0