My original assumption was that removing one bottle from aleph-1 bottles would still leave omega-1 bottles, so the song was naturally omega-0 long (but could equally well be omega-1, omega-2, etc). But other people's assumptions was that it referred to a _particular_ set of bottles, so even if at each stage, the number of bottles remaining was aleph-1, the limit would leave nothing.
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Date: 2013-10-28 10:41 am (UTC)My original assumption was that removing one bottle from aleph-1 bottles would still leave omega-1 bottles, so the song was naturally omega-0 long (but could equally well be omega-1, omega-2, etc). But other people's assumptions was that it referred to a _particular_ set of bottles, so even if at each stage, the number of bottles remaining was aleph-1, the limit would leave nothing.