1) The document discusses different number systems and their definitions of the number one. It suggests that for describing natural events and observations, the Fibonacci definition of one is most appropriate due to evidence of the Fibonacci sequence in nature. 2) The Fibonacci number one is defined as an infinite limit of ratios. This definition correlates with the Bernoulli base of natural logarithms. 3) For a mathematical description of nature to be accurate, the number system must comply with the natural conditions of the number one defined by both the Fibonacci sequence and natural logarithms.

1. Number Systems
Background: Numbers Systems is a post to explore number systems in general and for use in the
physical and computational sciences.
Post 1
The Number One
The are many ways to define the number one. Some of them can be described as circular
definitions, e.g. 1 = 2 – 1.
This post suggests the starting point (definition) of the number one is important for the specific
organization, purpose, or discipline that is employing a given number system.
Post 1 suggests the number system to describe nature, natural events, natural observations,
universal physical constants and so on, should be defined using the Fibonacci definition of the
number one. The suggested reason is the abundant evidence of the Fibonacci sequence in nature,
e.g. natural growth of trees, plants, flowers, and the consistent recurrence of the Fibonacci spiral
in many natural patterns whether Earthly or celestial.
The Fibonacci number one is defined by infinite limits of ratios. In that sense, and in a natural
sense, numbers are anticipated to be dimensionless.
Eq. 1
1 = 𝜙 + 𝛾
Eq. 2
1 =
[
1 +
2
5
3
1
5
2
8
3
13
5
21
8 . . . ^
1
𝛾
]
−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.
Post 2 is intended to further define the number one for application to natural laws and events.