User blog:Wythagoras/All my stuff

I have made some interesting stuff.

Dollars function
See blog post about dollars function.

Y function
Y(n) is defined as the maximal output of a notation uses n rules, and in the base rule only addition, multiplication and exponentation and in the other rules only recursion. For the final output of Y(n), you must place n in all the variables. default value is 0, no cheating etc.

Y(1) = 2, using f(a) = a+a

Y(2) ≥ 2048, using f(a,0) = a+a and f(a,b) = f(f(...(f(f(a,b),b-1),b-1)...),b-1)

Y(3) \(\geq f_{\varepsilon_0}(3)\)

Y(4) \(\geq f_{\Gamma_0}(4)\)

Y(5) \(\geq f_{\vartheta(\Omega^\omega)}(5)\)

Y(6) \(\geq f_{\vartheta(\Omega^\Omega)}(6)\)

Y(7) \(\geq f_{\vartheta(\varepsilon_{\Omega+1})}(7)\)

Y(8) \(\geq f_{\vartheta_{\Omega_{2}}}(8)\)

Y(9) \(\geq f_{\vartheta_{\Omega_{\omega}}}(9)\)

Y(10) \(\geq f_{\vartheta_{\Omega_{\Omega}}}(9)\)