Rule | Description | |

Framework: Type 1 Uninomial Unbounded Conducement Sequences Remark 5.1: ST: Sub-Term; SST: Sub-sub-term; SSST: Sub-sub-sub-term | ||

5.1 | Each sequence at a hierarchy is unbounded and the identity of its terms is identified by the ordinal of the terms (e.g. 3 | |

5.2 | Generation G = 1 (d = 0): each term is composed of one term in its internal structure | |

5.3 | Generation G = 2 (d = 1): each term has as many ST as its ordinal number, e.g. Term 3 has 3 sub-terms. | |

5.4 | Generation G = 3 (d = 2): each ST has as many SST as its ordinal number. | |

5.5 | Generation G = 4 (d = 3): each SST has as many SSST as its ordinal. | |

5.6 | Rules (5.1)-(5.6) are recursive with the effect of nesting within each hierarchy the structures of the numbers at its lower hierarchy―the regeneration product rule. | |

Generalisation: Types 2, 3 and 4 Unbounded Conducemental Sequences | ||

5.7 | Type 1 uninomial sequences all have the kernel of: $\langle 1\rangle $ but the kernel size of Types 2, 3 and 4 parent sequences have the kernel: $\langle \begin{array}{ccc}{T}_{1}& {T}_{2}& \begin{array}{ccc}{T}_{3}& \cdots & {T}_{\omega}\end{array}\end{array}\rangle $ , with their sizes, $\omega $ , may be less than, equal to and greater than the degree of parent sequences. | |

5.8 | The first term of the parent sequence will replace $\langle 1\rangle $ with ${T}_{1}$ , the second term will replace that with: ${T}_{1}+{T}_{2}$ ; the third term with: ${T}_{1}+{T}_{2}+{T}_{3}$ , $\cdots $ and the ${\omega}^{th}$ term with: ${T}_{1}+{T}_{2}+{T}_{3}+\cdots +{T}_{\omega}$ . Thereafter, the kernel will be replicated as a whole, i.e. for ${\left(\omega +1\right)}^{th}$ term, there is one additional term of ${T}_{1}+{T}_{2}+{T}_{3}+\cdots +{T}_{\omega}$ and for ${\left(\omega +2\right)}^{th}$ term, there are two additional terms of ${T}_{1}+{T}_{2}+{T}_{3}+\cdots +{T}_{\omega}$ and so on. Remark 5.2: Attention is drawn to the deep level of replication in this rule table. | |