Megafuga-

Megafuga- is a prefix used on a number n to indicate \(^nn\) using tetration (i.e. n pentated to 2) for the purpose of discussing how kids make up names for large numbers.A Fuga Really Big Numbers3.2.2 - The Fz, The Fuga & The Megafuga 
This prefix is a retronym for fuga- in response to the non-power associativity of exponentiation. Fuga- stands for \(\overbrace{n ↑ n ↑ n ↑ ... ↑ n}^n\), and is conjured for the purpose of how a kindergartener or primary grader can make up a number after being taught about powers. It was suggested by Stephen Houben, who asked, when hearing about Alistair Cockburn's fuga- prefix:
Since the ^ operation is not associative, i.e. \(\left(x^y\right)^z \not= x^{\left(y^z\right)}\), this begs the question whether Fuga(3) means \(\left(3^3\right)^3 = 19,683\) or \(3^{\left(3^3\right)} = 7,625,597,484,987\). Probably the latter, since the goal is to get big numbers....
Alistair Cockburn has kept fuga- as the former, and named the latter "megafuga-". He has edited this on his blog.
In Hyper-E notation, this is equal to E[n]1#n, and in Poly-cell notation, this is [n][n]<1>.
The first five values of megafuga-x are 1, 4, 7,625,597,484,987, 108.0723*10153, and 10101.3357*102,184. Houben noted, using a computer, that megafuga(4) is about \(4^{1.34 \times 10^{154}}\), somewhat larger than \(4^{10^{100}}\), and concluded that "computing all [the] digits of megafuga(4) will never happen." The decimal expansion of that number begins and ends with: 23,610,226,714,597,313,206............36,860,456,095,261,392,896 However, the number is far too large to write out all of the digits.
For megafuga-n:
== Sources ==
== See also ==
ja:メガフガ
zh:美卡福卡
Category:Prefixes
Category:Fuga- family
Category:Numbers discussed by Alistair Cockburn
Category:Numbers named by kids
Category:Tetrational growth rate