FYI: Two key generalizations can be constructed upon patterns evident in the

*"*,

__dialectical__

*purely**-*

*calculations" of my immediately-previous blog-entry here, which was entitled "*

__qual__itative**How to Calculate**[

__Dialectically__**and**

*purely**-*

*] --*

__qual__itatively**1**.

**) First**

*gene*ralization / theorem:

__|-|-|__**k+1**

**=**

__|-|-|__**k**

**[**

__|-|-|__**k**

**]**

**=**

__|-|-|__**k**

*"*

**of**"

__|-|-|__**k**

**=**

__|-|-|__**k**

*"*

**times**"

__|-|-|__**k**

**=**

|-|-||-|-|

**k**

**x**

__|-|-|__**k**

**=**

|-|-||-|-|

**k**

*"*

**squared***"*

**=**

|-|-||-|-|

**k^2**

**=**

*"*<<

**the**__>>,__

**aufheben**

**determinate**-__self__**negation**

**of**"

__|-|-|__**k**

**=**

**~**

__|-|-|__**k**.

This chain of equations, which constitutes the

**F**.

__.__

**E**__.__

**D***"*

**generic***, or*

**-**__meta__**evolution equations**"*"*

**generic***, defines the*

**r****"**__evolution__equations

__|-|-|__**k**as

*"*, that is, as

**self**-**reflexive****functions**"*"subject-*[

*verb-*]

*object identical"*operators, expressed "ideo-gram-ically", as a

*"*

**-**__dialectical__**algebraic**

**-**__meta__*, rather than in the form of a "phono-gram-ically"-expressed, phonetic sentence(s)*

**model**"*"*

**-**__meta__*.*

**model**"Indeed, the

**F**.

__.__

**E**__. "Dyadic Seldon Function" for the__

**D***--*

**generic**__dialectic__

__|-|-|__**k**

**=**

__|-|-|__**0^(2^k)**

**= [**

__q__/1 ]**^(2^k)**

-- is the

*to the*

**general solution***"*

*(*

__meta__-finite difference equation*s*)" stated above.

**2**.

**)**

**Second**The

*gene*ralization / theorem:**W**hole-number exponent, or power, of the <<

*>> equals the number of ontological categories summed [non-amalgamatively] in the expansion of that power-expression.*

**arche'**The <<

*>>, or originating, initiating, ever-present-origin ontological category of a*

**arche'***, is*

__dialectical__categorial progression**represented by the**

*generically**"meta-numeral"*

**purely**-__qual__itative**in the**

__q__/1**N**

**"**

__Q__**First**

**Dialectical***, whose "meta-number" set is --*

**Arithmetic**"**N**

__Q____=__**{**

**,**

__q__/1**,**

__q__/2**,**

__q__/3**, . . .**

__q__/4**}**, given --

**N**

__=__**{**

**1**,

**2**,

**3**,

**4**, . . .

**}**

-- as the number-set of the "

**N**atural" Numbers.

The number-set known as the "

**W**hole numbers" is --

**,**

W

W

__=__{ 0**1**,

**2**,

**3**,

**4**, . . .

**}**.

Thus --

__|-|-|__**0^(2^0)**

**= [**

__q__/1 ]**^(2^0)**

**=**

**[**

__q__/1 ]**^1**

**=**

__q__/1**;**

__|-|-|__**0^(2^1)**

**= [**

__q__/1 ]**^(2^1)**

**=**

**[**

__q__/1 ]**^2**

**=**

__q__/1**+**

__q__/2**;**

__|-|-|__**0^(2^2)**

**= [**

__q__/1 ]**^(2^2)**

**=**

**[**

__q__/1 ]**^4**

**=**

__q__/1**+**

__q__/2**+**

__q__/3**+**

__q__/4**;**

__|-|-|__**0^(2^3)**

**= [**

__q__/1 ]**^(2^3)**

**=**

**[**

__q__/1 ]**^8**

**=**

__q__/1**+**

__q__/2**+**

__q__/3**+**

__q__/4**+**

__q__/5**+**

__q__/6**+**

__q__/7**+**

**,**

__q__/8etc.

The two statements above can, of course, be proven deductively, given the full axioms-set of the

**N**

**, or of the**

__Q__**W**

**,**

__Q____,__

**dialectical***arithmetic.*

**purely**-__qual__itativeRegards,

Miguel

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