Ultron

The ultron is defined like so:
# Define \(u_{0,1}\) as \(h_{100}(10,10,10,10,10,10,10,10,10,10)\), using the hyperlicious function.
# Define \(u_{x,1}\) as \(h_{100}(\underbrace{10,10,\ldots,10,10}_{u_{x - 1,1}})\).
# Define \(u_{0,2}\) as \(\underbrace{u_{u_{u_{\ddots_{100,1}},1},1}}_{10 \text{ copies of } u}\).
# Define \(u_{x,2}\) as \(\underbrace{u_{u_{u_{\ddots_{100,1}},1},1}}_{u_{x - 1,2} \text{ copies of } u}\).
# Define \(u_{0,3}\) as \(\underbrace{u_{u_{u_{\ddots_{100,2}},2},2}}_{10 \text{ copies of } u}\).
# Define \(u_{x,3}\) as \(\underbrace{u_{u_{u_{\ddots_{100,2}},2},2}}_{u_{x - 1,3} \text{ copies of } u}\).
# Continuing this process, the ultron is \(u_{100,100}\).
The ultron is comparable to \(f_{\omega+200}(100)\) in the fast growing hierarchy.
== Sources ==
== See also ==
*ultronplex
ja:ウルトロン
Category:Numbers
Category:Numbers from A googol is a tiny dot
Category:Googol series
Category:Linear omega level