![𝑇1→8 = (1 + 𝑅 𝐸
2
1⁄ 3
2⁄ 5
3⁄ 8
5⁄ 13
8⁄
)
𝑇3→8 = 1 + 𝑅 𝐸
8
5⁄ 13
8⁄
As in Post 2
13 = (1 +
𝛾∞
𝑓
𝑇3→8
)
−1
(1 +
𝛾3
𝑓
𝑇3→8
)
+1
Then for F(n) = D = 3:
13 =0.999268
For example:
33 = [1(0.999268) + (1 +
𝛾∞
𝑓
𝑇3→8
)
−1
𝑥 (1 +
𝛾3
𝑓
𝑇3→8
)
+1
] 𝑥 3(0.999268)
33 = 2.99792
and so on for other integers where F(n) = D = 3.
Post 4 is intended to clarify nomenclature through additional examples of the Fibonacci
definition of one.](https://image.slidesharecdn.com/663cb1a0-25b7-499a-b446-8a5b968bc005-160229035632/85/Post_Number-Systems_3-2-320.jpg)
Post_Number Systems_3
- 1. Number Systems Background: Number Systems is a post to explore number systems in general and for use in the physical and computational sciences. Post 3 The Number One for Fibonacci n F(n) Post 2 has established: 1 𝐷 = (1 + 𝛾(∞) 𝑓{𝐷} 𝑇𝐷→(𝐷+𝛥2𝐷) ) −1 (1 + 𝛾(𝐷+𝛥2𝐷) 𝑓{𝐷} 𝑇𝐷→(𝐷+𝛥2𝐷) ) +1 1 𝐷 = (1 + 𝛾∞ 𝑓 𝑇𝐷 ) −1 (1 + 𝛾 𝐷 𝑓 𝑇𝐷 ) +1 For natural events, this definition should correlate to the Bernoulli base of natural logarithms: ∫ 1 𝑥 𝑑𝑥 𝑒 1 = 1 where lim 𝑛→∞ (1 + 1 𝑛 ) 𝑛 = 𝑒 A mathematical description of nature should not be accurate unless the number system complies with both natural conditions of the number one shown above. 𝐹 = {0, 1: 1, 2, 3, 5, 8, 13, 21, 34, 55, … } To continue required mathematical rigor for natural events, we would need to define values of one that apply to individual Fibonacci integers n in addition to the universal value of one = 1∞. This is difficult nomenclature. An example of 1D for D = 3 where n also = 3, n3 = D = 3: F = {0,1: 1, 2, 3, 5, 8, 13, 21, 34, 55, …} 1 𝐷 = (1 + 𝛾∞ 𝑓 𝑇𝐷 ) −1 (1 + 𝛾 𝐷 𝑓 𝑇𝐷 ) +1 Where D = 𝐹(3) = 3 ƒ = γ-1 {3} = 3 1 ^ 5 2 𝑇1→3 = (1 + 𝑅 𝐸 2 1⁄ 3 2⁄ 5 3⁄ )
- 2. 𝑇1→8 = (1 + 𝑅 𝐸 2 1⁄ 3 2⁄ 5 3⁄ 8 5⁄ 13 8⁄ ) 𝑇3→8 = 1 + 𝑅 𝐸 8 5⁄ 13 8⁄ As in Post 2 13 = (1 + 𝛾∞ 𝑓 𝑇3→8 ) −1 (1 + 𝛾3 𝑓 𝑇3→8 ) +1 Then for F(n) = D = 3: 13 =0.999268 For example: 33 = [1(0.999268) + (1 + 𝛾∞ 𝑓 𝑇3→8 ) −1 𝑥 (1 + 𝛾3 𝑓 𝑇3→8 ) +1 ] 𝑥 3(0.999268) 33 = 2.99792 and so on for other integers where F(n) = D = 3. Post 4 is intended to clarify nomenclature through additional examples of the Fibonacci definition of one.