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 4
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.
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.

2. An example using a real number instead of an integer:
6.6260700E-34
6.6260700E-34 = 6.6260700 x (1 − 𝑅 𝐸
3
1⁄
5
2⁄
) x 10-34
From post 2, we could also write:
6.6260700E-34 = 6.6260700 x (1∞ − 𝑅 𝐸
𝑓{3}
) x 10-34
and so on for other real numbers where F(n) = D = 3.
Post 5 is intended to further clarify nomenclature through other examples of the Fibonacci
definition of one for F(n) = D = 3.