The beginning is a term from set theory and order theory.
A class is called the beginning of the ordered class if . T {\ displaystyle T} ( K , < ) {\ displaystyle (K, <)} ∀ x ∈ K ∀ b ∈ T : ( x < b ⇒ x ∈ T ) {\ displaystyle \ forall x \ in K \ \ forall b \ in T: (x <b \ Rightarrow x \ in T)}
Every ordered class is divided into two disjoint subclasses:, where . K {\ displaystyle K} K = T ∪ ( K ∖ T ) {\ displaystyle K = T \ cup (K \ setminus T)} ∀ x ∈ T ∀ y ∈ ( K ∖ T ) : ¬ ( y < x ) {\ displaystyle \ forall x \ in T \ \ forall y \ in (K \ setminus T): \ neg (y <x)}
Above quantity
