open problems survey Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022 11/01/2022, 06:33 AM (This post was last modified: 12/22/2022, 07:13 AM by Catullus.) (07/12/2022, 05:39 AM)JmsNxn Wrote: (07/12/2022, 03:22 AM)Catullus Wrote: Conjecture: The standard extension of exponentiation is the only extension of exponentiation, such that a to the power of x is totally monotonic, For all real a between one and zero non inclusive, and for all real a. OHHHHHH CATULLUS!!! This is a good one. I'd suggest an old thread by me on MathOverflow, but it's lost in all the overflow.I think that this is the thread. Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022 12/22/2022, 06:37 AM (This post was last modified: 12/22/2022, 07:08 AM by Catullus.) Conjecture: $$\forall a,b\in\Bbb N-1\:\lim_{t\to\infty}g_a(b\uparrow\uparrow\lfloor t\rfloor)\in\overline{\Bbb Q}\iff b\div a\in\Bbb N$$, where $$g_a$$ denotes the a-ary van der Corput sequence. Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ « Next Oldest | Next Newest »

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