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Nov 7, 2019 at 15:55 comment added Honza @ Iosif Pinelis Thanks for your very elegant proof - much simpler than Karlin's; it seems that to find $\omega_1$ you would not even need the last limit! You are right: my question should have mentioned that $\omega_1$ may be infinite, which then makes the corresponding limit meaningless.
Nov 7, 2019 at 3:08 vote accept Honza
Nov 6, 2019 at 5:09 history edited Iosif Pinelis CC BY-SA 4.0
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Nov 6, 2019 at 2:15 history edited Iosif Pinelis CC BY-SA 4.0
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Nov 6, 2019 at 2:03 history answered Iosif Pinelis CC BY-SA 4.0