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+--- Thread: open problems survey (/showthread.php?tid=162)
RE: open problems survey - Catullus - 11/01/2022
(07/12/2022, 05:39 AM)JmsNxn Wrote:I think that this is the thread.(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.
RE: open problems survey - Catullus - 12/22/2022
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.