Encoding

An encoding is a way of representing a number or expression in terms of another (usually simpler) one. However, multiple expressions can also be encoded as a single expression, as in, for example,

$$(a,b)\equiv {\textstyle{1\over 2}}[(a+b)^2+3a+b]$$

which encodes $a$ and $b$ uniquely as a single number.

$a$	$b$	$(a,b)$
0	0	0
0	1	1
1	0	2
0	2	3
1	2	4
2	0	5

See also Code, Coding Theory