Editing Conway chained arrow notation (section)

==Interpretation==
One must be careful to treat an arrow chain ''as a whole''. Arrow chains do not describe the iterated application of a binary operator. Whereas chains of other infixed symbols (e.g. 3&nbsp;+&nbsp;4&nbsp;+&nbsp;5&nbsp;+&nbsp;6&nbsp;+&nbsp;7) can often be considered in fragments (e.g. (3&nbsp;+&nbsp;4)&nbsp;+&nbsp;5&nbsp;+&nbsp;(6&nbsp;+&nbsp;7)) without a change of meaning (see [[associativity]]), or at least can be evaluated step by step in a prescribed order, e.g. 3<sup>4<sup>5<sup>6<sup>7</sup></sup></sup></sup> from right to left, that is not so with Conway's arrow chains.

For example:
* <math>2\rightarrow3\rightarrow2 = 2\uparrow\uparrow3 = 2^{2^2} = 2^4=16</math>
* <math>2\rightarrow(3\rightarrow2) = 2^{3^2} = 2^9 = 512</math>
* <math>(2 \rightarrow3)  \rightarrow2 = (2^3)^2 =8^2=64</math>

The sixth definition rule is the core: A chain of 4 or more elements ending with 2 or higher becomes a chain of the same length with a (usually vastly) increased penultimate element. But its ''ultimate'' element is decremented, eventually permitting the fifth rule to shorten the chain. After, to paraphrase [[Donald Knuth|Knuth]], "much detail", the chain is reduced to three elements and the fourth rule terminates the recursion.