Definition and Overview
A Conway chain (or chain for short) is defined as follows:
- Any positive integer is a chain of length 1.
- A chain of length n, followed by a right-arrow → and a positive integer, together form a chain of length .
Any chain represents an integer, according to the four rules below. Two chains are said to be equivalent if they represent the same integer.
If and are positive integers, and is a subchain, then:
- The chain represents the number .
- represents the exponential expression .
- is equivalent to .
- is equivalent to
(with p copies of X, p − 1 copies of q, and p − 1 pairs of parentheses; applies for q > 0).
Note that the last rule can be restated recursively to avoid the ellipses:
- 4a.
- 4b.
Read more about this topic: Conway Chained Arrow Notation
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)