Bird's Proof

Bird's Proof is a theorem by Chris Bird that states that:Bird's proof: Note that, at the time of the writing of the proof, Bowers' function defined {a,b} as the sum of a and b, while Bird redefined it as \(a^b\), considering it to be a different function. Bowers later revised his own notation to match Bird's, so the notations are identical.http://www.mrob.com/users/chrisb/Proof.pdfArray Notation
\[\forall a \geq 3, b \geq 2, c \geq 1, d \geq 2: \{a, b, c, d\} > \underbrace{a \rightarrow a \rightarrow \ldots \rightarrow a \rightarrow a}_d \rightarrow (b - 1) \rightarrow (c + 1)\]
using array notation and chained arrow notation.
In other words, four entries of array notation are comparable to chained arrow notation, but five entries far surpass it.
It was published in his paper "Array Notations for Super Huge Numbers", and was named by Jonathan Bowers on his website.
== Sources ==
== See also ==
*Array Notation
* Knuth Arrow Theorem
ja:バードの証明
Category:BEAF
Category:Theorems