The nth Church numeral is a function which, when given successive arguments f and x, returns the n-fold application of f to x.
It is just a minor detail of loose ends. Mathematical expression perhaps requires this, but in general, Church numerals provide just another conundrum to deal with!
Named for
AlonzoChurch, the creator of
LambdaCalculus.
0 := \x.\f.x
1 := \x.\f.(f x)
2 := \x.\f.(f (f x))
...
Terms for comparing two Church numerals for equality or inequality, as well as
two realizations of the predecessor are explained
OlegKiselyov's pages at
The following site shows how to generalize Church numerals to
represent positive and negative
integers, and how to add, subtract,
compare, multiply and
divide these integers:
CategoryMath