The E-theory straightforward, and in short

 

Different x (phenomena) owns different x (properties):

 

x≠y; [{x}x]≠[{x}y]:

 

x=y; [{x}x]=[{x}y].

 

x and y is in the latter case one and the same (unique) x, because all of x och y:s properties are identical:

 

Up) x=[unique x]:

 

Different x owns at least one, one another separating property (for example x=[{x}x]≠y={x}).

 

Up) (x)=x.

 

Ip) x=x.

 

Kp) x≠x (but x=x (Ip), a unique x, given Up).

 

Further, is the derivation rule defined(/assumed) that a relation doesnt change if x and y are changed identically:

 

Fp) [x~y]≠[x~y].

 

Given this rules/principles, the following is defined:

 

Nothing=[propertyless x]:

 

xNothing; x=[propertylessness].

 

Per definition of Nothing (as propertyless) though, the following is valid:

 

xNothing.

 

So, [xNothing]=[xNothing], a contradiction, contrary to Kp(/Ip):

 

T1) Nothing dont exist (at all).

 

To really underline T1, Nothing is assumed to (be able to) exist:

 

Nothing=existence:

 

propertylessness=existence non-existence=[at least one property]:

 

Nothing=non-existence; Kp.

 

Which verifies T1.

 

Given T1 the following is valid, where 0* owns (is) one property, p two:

 

Nothing<0*<p; 0*=[non-extension (without position)], p=[non-extension with position (point)].

 

0* is defining (is) an extension, assume not:

 

0*≠d(p,p)=[a curve between p and p (an extension, consisting of p:s continuously (lim p=p; pp) in a row]:

 

0*+d(p,p)≠d(p,p)+d(p,p); Fp:

 

0*+d(p,p)≠d(p,p); Up:

 

d(p,p)≠d(p,p), given that 0* is a non-extension, which accordingly not adds anything to d(p,p) (an extension):

 

0*=extension; Kp.

 

Given this, assume:

 

0*<*=[smallest infinite extension]:

 

0*+∞*<∞*+∞*; Fp:

 

0*+∞*<∞*; Up:

 

0*≥∞*; Kp.

 

Given this, assume:

 

0*>∞*:

 

0*+0*+∞*>∞*+0*+∞*; Fp:

 

0*+∞*>0*+∞*; Up (here its evidently indifferent where ∞* is unified, which not always is the case, because it can be of immense im-portance on which side a variable is: [x~y]=[y~x], (symmetry) is not always (seldom) valid):

 

A) 0*=*; Kp.

 

If * owns a border (outer or internal), at least 0* exists beyond this border, given T1:

 

* *+0*.

 

And:

 

*+0*>*:

 

*+*>*; A:

 

*>*; Up:

 

* is (continuously/homogenously) borderless; Kp.

 

Assume:

 

E>0*:

 

E+E>0*+E; Fp:

 

E>0*+E; Up:

 

E0*; Kp:

 

E=0*; (E)<0* defines the non-existing Nothing (given T1):

 

E=*; A:

 

T2) E=0*=*.

 

Assume:

 

x≠E; xE (xE, given T2, defines x in another dimension (or in other dimensions) than E, which is excluded (as absurd)):

 

x+E≠E+E; Fp:

 

E≠E; Up:

 

I) x=E; Kp.

 

I means that every (possible) possibility is eternal.

 

Given I och T2 per definition defined x≠E(; xE) is finite, simpliciter because E is a smallest infinity. More rigorously, assume not:

 

x≠E; x=[infinite x(E)]:

 

x+E≠E+E; Fp:

 

E≠E; Up:

 

x=[finite x]; Kp.

 

Given this and T1, that nothing can arise from the non-existing Nothing, and an completely calm E, with no waves, mx, smallest x, must be created through (local; T2) contraction initiated by E:

 

E mx:

 

mx=[{mv}mx]; mv=[smallest volume].

 

mxmv as volume, and more compact than mv (or a (uncompressed) volume v>mv). If mx isnt a volume, mx is either a point (p), a cur-ve (k=d(p,p)), or a surface(/plane), for example y=d(k,p); pk. p, k och y are (homogenously) one with E, only something per se, if it is defined so to be, if the mind, so to say, (before its inner eye) draws it in the space:

 

mx are more compact volume (than v(mv); mx owns more density than v).

 

mv are assumed to own exactly the same properties (position excluded), which given I means all properties to define/create all (material) x(E) which can occur in E (more properties than necessary/sufficient for this, is it redundant to define mv to own). And it also, in accor-dance with Up (see below), means that the same {mv} owns the same properties, not different properties, which for example means that the same {mv} cant, in one case define a stable mx, in another case define an unstable mx, which is completed, more rigorously, assume mx to consist of only one mv more than mx:

 

mx=[({mv}+mv)mx]; mx=[{mv}mx]:

 

mx-mv={mv}=0^ (Up disregarded, mv shall be interpreted as being withdrawn (separated) from mx).

 

The same {mv} is thus regarding mx unstable, regarding mx stable, which contradicts that mv, and with that also {mv} (in accordance with Up), owns exactly the same properties:

 

Homogenous atomism prevails, all mx are exactly the same (owns identical properties, position disregarded):

 

Ha) x=(x/mx).

 

A validity of Ha which then rests upon the assumption that (all) mv owns identical properties (position disregarded), which must be rega-rded as a rational assumption.

 

Given this, the (E-)World can quite easily be further defined(/developed), specifically can mx be more rigorously defined, how they be-have as mx per se, and as building x={mx}.

 

Given Ha, Fp can be shown to be valid at Ha-level (x assumed to be the atomistic (logical) constituent(/component) (x in Ha)):

 

[x~y]≠[x~y]: