Comment by jhanschoo
1 day ago
Nitpick:
s/must shrink/must eventually shrink, after finitely many n/
Equivalently, must go to zero in the limit.
1 day ago
Nitpick:
s/must shrink/must eventually shrink, after finitely many n/
Equivalently, must go to zero in the limit.
depends on what you think shrink means. If you mean decreasing, that's false even eventually.
Hmm you're right it's no more rigorous what I said. (For each positive number the expression must eventually, after finitely many terms, always be smaller than that number thereafter)
But you're not right in that the upper bound of that expression eventually stops decreasing, in fact for simple f and g as long as f is positive and eventually bounded by g the expression will decrease infinitely often if my intuition is correct
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