User blog comment:Ytosk/Trying to define Bowers' K(n) systems/@comment-37556263-20191031223720

If you're going to use \(MK(n,m)\) to define Oblivion, perhaps \(MK^{10^100}(10^{100},10^{100})\) could be MK-Ultra, where \(MK^{x}(n,m)\) refers to the fractal nesting of \(MK(n,m\) x-times.

For instance,


 * \(MK^{1}(n,m) = MK(n,m)\)
 * \(MK^{2}(n,m) = MK(MK(n,m),MK(n,m))\)
 * \(MK^{3}(n,m) = MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m)))\)
 * \(MK^{4}(n,m) = MK(MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m))),MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m))))\)
 * \(MK^{5}(n,m) = MK(MK(MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m))),MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m)))),MK(MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m))),MK(MK(MK(n,m),MK(n,m)),MK(MK(n,m),MK(n,m)))))\)
 * etc...

Now imagine \(MK^{10^{100}}(10^{100},10^{100})\). Yeah, it's big. Although it seems you may have more work to do in the formality department. Still awesome to try to figure out formal versions of these numbers that have been around for so long and with no clear resolution! Keep up the good work!