Notes concerning the $λ$ calculus

$λ$ terms:

Variable: $x$
Abstraction: $(λx.M)$
Application: $(MN)$

Reduction operations:

$α$ reduction: $λx.M → λy.[y/x]M$
$β$ reduction: $(λx.M)N → [N/x]M$

Church numerals:

$0 := λfx.x$
$1 := λfx.fx$
$2 := λfx.f(fx)$