According to the Dayhoff model, orthologous sequences evolving in two different lineages will asymptotically approach the saturation percent identity value characteristic of alignments of unrelated sequences (formula 1).
In the brilliant opening sequence the formula seems to work beautifully.
For any sequence recurrence formula, the Smarandache-Pascal derived sequence { T n } of { b n } is defined by T n + 1 = ∑ k = 0 n ( n k ) ⋅ b k + 1 for all n ≥ 2, where ( n k ) = n ! k ! ( n − k ) ! denotes the combination number.
Call this number n. Insert these values into the equation: Insert these values into the equation: If you know the last term, l, of the sequence, the formula S = 0.5n(a+l) can be used instead.
As will appear later (see below Axiomatization of PC), the question whether a sequence of formulas in an axiomatic system is a proof or not depends solely on which formulas are taken as axioms and on what the rules are for deriving theorems from axioms, and not at all on what the theorems or axioms mean.
A proof is any finite sequence of formulas, each of which is an axiom or an immediate consequence, by a rule of inference, of (one or two) preceding formulas of the sequence.
A skeptical solution for ⟨ O, C ¯, ψ ⟩, is a sequence of formulas such that φ1,…, φ n such that: 1. φ i ∈C i, for i≤n 2.
A credulous solution for ⟨ O, C ¯, ψ ⟩, is a sequence of formulas such that φ1,…, φ n such that: 1. φ i ∈C i, for i≤n 2.
The way the manipulator tries to bring this about is by specifying a sequence of formulas to be provided to the believer as information to be incorporated.
Consequently, it is also possible to decide for any given finite sequence of formulas, whether it constitutes a genuine derivation, or a proof, in the system given the axioms and the rules of inference of the system.
