The Etheory straightforward, and in short
Different x (phenomena) owns different x’ (properties):
x≠y; [{x’}Îx]≠[{x’}Îy]:
x=y; [{x’}Îx]=[{x’}Îy].
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 doesn’t change if x and y are changed identically:
Fp) [x’~y’]≠[x~y].
Given this rules/principles, the following is defined:
Nothing=[propertyless x]:
x’ÎNothing; x’=[propertylessness].
Per definition of Nothing (as propertyless) though, the following is valid:
x’ÏNothing.
So, [x’ÎNothing]=[x’ÏNothing], a contradiction, contrary to Kp(/Ip):
T1) Nothing don’t exist (at all).
To really underline T1, Nothing is assumed to (be able to) exist:
Nothing=existence:
propertylessness=existence ® nonexistence=[at least one property]:
Nothing=nonexistence; Kp.
Which verifies T1.
Given T1 the following is valid, where 0* owns (is) one property, p two:
Nothing<0*<p; 0*=[nonextension (without position)], p=[nonextension 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’; p®p’) 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 nonextension, 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 it’s evidently indifferent where ∞* is unified, which not always is the case, because it can be of immense importance 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’:
E≤0*; Kp:
E=0*; (E)<0* defines the nonexisting Nothing (given T1):
E=∞*; A:
T2) E=0*=∞*.
Assume:
x≠E; xÎE (xÏE, 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(; xÎE) is finite, simpliciter because E is a smallest infinity. More rigorously, assume not:
x≠E; x=[infinite x(ÎE)]:
x+E≠E+E; Fp:
E≠E; Up’:
x=[finite x]; Kp.
Given this and T1, that nothing can arise from the nonexisting 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}Îmx]; mv=[smallest volume].
mx≥mv as volume, and more compact than mv (or a (uncompressed) volume v>mv). If mx isn’t a volume, mx is either a point (p), a curve (k=d(p,p’)), or a surface(/plane), for example y=d(k,p’’); p’’Ïk. 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 accordance with Up’’ (see below), means that the same {mv} owns the same properties, not different properties, which for example means that the same {mv} can’t, 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)Îmx]; mx’=[{mv}Îmx’]:
mxmv={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 regarded 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 behave as mx per se, and as building x={mx}.
Given Ha, Fp can be shown to be valid at Halevel (x assumed to be the atomistic (logical) constituent(/component) (x’ in Ha)):
[x’~y’]≠[x~y]:
