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[[Introduction and Foundation Concepts for Itoequations]]

==See also:==

[[Itoequations]], [[Oriequations]], [[Idoequations]], [[Coriequations]],  [[Citoequations]],  [[Vitoequations]],  [[Fitoequations]],  [[Isoequations]],  [[Enhaequations]],  [[Musequations]],  [[Insiequations]],  [[Tritoequations]],  [[Nrgequations]],  [[Comboequations]], and  [[Simiequations]],

[[Itosynchronization equations]], [[Itofuturality equations]], [[Itohistorality equations]], [[Itotimultiplicity equations]], [[Itocelerity equations]], [[Itoquondamality equations]], [[Itoprospectality equations]], [[Itosimultaneousness equations]], [[Itoretrogression equations]], [[Itotemporality equations]], [[Itorepetition equations]] [[Itoreversion equations]], [[Itoprogression equations]], [[Itosucession equations]],

[[Fazequations]]  [[physiequations]], [[physaequations]], [[awarequations]], [[mentaequations]], [[ixpequations]], [[epiequations]],

[[fazmapping]], [[itomapping]], [[itofazmapping]], [[itomapping equations]], [[fazmapping equations]], [[itofazmapping equations]],

[[faztransformation]], [[itotransformation]], [[itofaztransformation]], [[itotransformation equations]], [[faztransformation equations]], [[itofaztransformation equations]]


[[Fazsynchronization equations]], [[Fazfuturality equations]], [[Fazhistorality equations]], [[Faztimultiplicity equations]], [[Fazcelerity equations]], [[Fazquondamality equations]], [[Fazprospectality equations]], [[Fazsimultaneousness equations]], [[Fazretrogression equations]], [[Faztemporality equations]], [[Fazrepetition equations]] [[Fazreversion equations]], [[Fazprogression equations]], [[Fazsucession equations]],

[[Itoinception equations]], [[Itoexordium equations]], [[Itocreation equations]], [[Itomodality equations]], [[Itoautochthonality equations]], [[Itocausality equations]], [[Itoerudition equations]],

[[Itocontinuance equations]], [[Itoextension equations]], [[Itocontinuity equations]], [[Itodiscontinuity equations]], [[Itoidentity equations]], [[Itosimidentity equations]], [[Itosimicontinuance equations]], [[Itosimiextension equations]], [[Itosimicontinuity equations]], [[Itosimidiscontinuity equations]],

[[Itoconvergence equations]], [[Itodivergence equations]], [[Itomultivergence equations]], [[Itosimiconvergence equations]], [[Itosimidivergence equations]], [[Itomultisimivergence equations]], [[itocrossdivergence equations]], [[itocrossconvergence equations]], [[itosimimultivergence equations]], [[itocrossmultivergence equations]], [[itosimicrossmultivergence equations]],

[[Fazconvergence equations]], [[Fazdivergence equations]],  [[Fazmultivergence equations]], [[Fazsimiconvergence equations]], [[Fazsimidivergence equations]], [[Fazmultisimivergence equations]], [[Fazcrossdivergence equations]], [[Fazcrossconvergence equations]], [[Fazsimimultivergence equations]], [[Fazcrossmultivergence equations]], [[Fazsimicrossmultivergence equations]],

[[Symbolic definitions]],[[ Symbolic definitions part2]]

==[[Symbolic definitions]]==

In this section we deal with the construction and beginning development of the mathematical representation of some of the predictions, principles, and properties of [[originals]], [[idoriginals]], and [[cidentireplicas]], and their interrelationships, that were developed in the other areas of this website. These concepts are developed into equations that are called [[oriequations]], [[idoequations]], and  [[citoequations]]. These terms means that they are equations that deal with [[originals]], [[idoriginals]],  [[cidentireplica]]s and the identireplica theory of consciousness. Scientists make predictions, based on a theory, on how things in nature will function. If these predictions are universal enough it can be stated as a principle. If these predictions and principles deal with this or another universe they become properties of that universe. I believe that a certain set of these citoequations apply to this universe that we live in. It will be just as important of a scientific development if scientists find that this set of citoequations do not apply to this universe. This is because, if these equations are not applicable to this universe, the consequences will result in an entirely different possible future for mankind or all conscious beings in this universe.

This chapter creates an area of mathematics that deals with consciousness and ixperiencitness.

The equations can be true or false for different real universes or different [[modal universes]]. The ones that are true for this universe will have to be scientifically proven or disproven. There will be many equations that can be generated with this mathematics of consciousness that are not true for this universe. An example of this in arithematic is 1+1 = 2 is considered true in this universe but arithematic has the ability to create any number of other equations of the form 1+1 = n where n is any number. For example 1+1 = 5. This is not considered to be true in this universe. But in binary 1+1= 10. Or in the physical world 1 cup sugar plus 1 cup water does not equal 2 cups sugar water. Arithematic has the ability to generate relationships (concepts --knowledge) that are not related to any reality.


Terms will be labeled as Tn, relational operators will be labeled as Rn, functional operators will be labeled as Fn and the logical operators will be labeled Ln . The subscript variable n will start at one and increase in number as they are encountered in this chapter. A term is a name for a [[theocept]]. A theocept is a theoretical concept that can represent vast amounts of knowledge in any possible way.  A theocept can be a functional, relational, or logical operator among other things. 

Each term is a [[theocept]] -- a theoretical concept -- an arrangement of epistemological knowledge.

A combination or other arrangement of terms can be a term.

'''Terms, properties, relational, functional, and logical operators for itoequations.'''


'''The '''Terms''' or names for the physical objects or [[itobodies]]'''

T0:  [[Ito]], stands for the [[itoidentireplica]].

T1:  [[Ori]], stands for the [[original]].

T2:  [[Ido]], stands for an [[idoriginal]].

T3:  [[Cori]], stands for the [[coriginal]].

T4:  [[Cito]], stands for the [[cidentireplica]].

T5:  [[Vito]], stands for the [[videntireplica]].

T6:  [[Fito]], stands for the [[fidentireplica]].

T7:  [[Iso]], stands for the [[isoidentireplica]].

T8:  [[Enha]], stands for the [[enhaidentireplica]].

T9:  [[Mus]], stands for the [[musidentireplica]].

T10:  [[Insi]], stands for the [[insidentireplica]].

T11:  [[Trito]], stands for the [[tridentireplica]].

T12:  [[Nrg]], stands for the [[nrgidentireplica]].

T13:  [[Combo]], stands for the [[comboidentireplica]].

T14:  [[Simi]], stands for the [[simidentireplica]].


'''Properties of the [[itobodies]]'''

P1: X represents [[ixperiencitness]]

P2: C represents [[consciousness]]

P3: B represents behavior

P4:  O, defines the exact original that the term is defined (created) from. We call it the [[Original template]].

P5:  U, defines the universe and universal laws in it.  

P6:  E,  defines the exact matter and energy it is made of and placement over time.

P7:  D,  defines the exact orientation, dimensionality or space it exists in over time.

P8:  T  defines the exact time the body exists in and other time related concepts.

P9:  S, defines the [[exact structure]] of the object or body at any time.

P10: F, defines the [[exact functioning]] of the object or body over time and change in structure over time. The sequential sum of the change in structure over time.


'''Relational operators'''

A relational operator relates that particular concept that it is a relational operator of. 

R1: == means is the same identical thing or identically the same in every possible way. It is the sum of =P=, =M=,=B=, =N=,etc.

R2:  =P= means physically identical same matter and energy, same place, same time.

R3: =M= this is the relational symbol that means mentally equal -- all aspects of mentality.

R4:  =B= This is the relational operator for behavioral identity. This means that all behavior is identical.

R5:  =N= This is the relational operator that represents name equality. This means that the two terms have the same name. The concept of name reduction (replacement) is one name can be reduced to another when all factors or terms are equal.

R6    =O= This is the relational operator that represents using the same original as the template for knowledge, potential creation, or creation. “You”

R7:   =U= This is the relational operator that represents being in the same universe with the same universal laws.

R8:   =E=  This is the relational operator that represents materially  synchronized -- made of the same matter and energy in the same exact placement over the time period that is covered in the equation.

R9:    =D= This is the relational operator that represents dimensionally synchronized -- in the same place with the same orientation over the time period that is covered in the equation.

R10:   =T= This is the relational operator that represents time equality. This means that the two objects are in time synchronization

R11:  =S= This is the relational operator for structural identity.

R12:  =F= This is the relational operator for functional identity. This means that the functioning is identical.  

R13:  =K= is the  relational operator for knowledge identity. There are many types of knowledge that deal with different aspects of .

R14:  =Im= is the  relational operator for isomorphic functioning and structure. This means that they will produce the same awarepath with a different physipath. Isoidentireplicas will have this relationship

R15:  =Fg= is the  relational operator for fragmentation. This means that they will produce the same awarepath with a fragmented physipath. Fidentireplicas will have this relationship

R16  =C= is the  relational operator for conscious identity.

R17   =X= is the  relational operator for [[ixperiencitness]] identity.

'''Functional Operators'''

A functional operator operates on the object within the brackets. Every relational operator has a functional meaning.

F1:  P{   } is a functional operator that means the physical properties of the object with in the brackets. 

F2:  M{   } is a functional operator that means all the mentality of term, object, or theocept within the brackets.

F3:  B{   } is a functional operator that means the behavior of the term, object, or theocept  with in the brackets.

F4: N{   } is a functional operator that means the name of the term, object, or theocept with in the brackets.

F5:  O{   } is a functional operator that means the [[original]] that the term, object, or theocept with in the brackets is defined by.

F6:  U{   } is a functional operator that means the universe and or universal laws of the term, object, or [[theocept]] with in the brackets.

F7:  E{   } is a functional operator that means the exact  matter /energy and its placement, of the term, object, or theocept with in the brackets.

F8:  D{   } is a functional operator that means the exact placement and orientation of the term, object, or theocept with in the brackets.

F9:  T{   } is a functional operator that defines the exact time the term, object, or theocept exists in, with in the brackets. [[Theobject]] --theoretical object

F10:  S{   } is a functional operator that means the structure of the term, object, or theocept with in the brackets.

F11:   F{   } is a functional operator that means the functioning  of the term, object, or theocept with in the brackets.

F12:  K{   } is a functional operator that means the knowledge of the term, object, or theocept with in the brackets. 

F13:  C{   } is a functional operator that means the [[consciousness]] produced by  the object with in the brackets.

F14:  X{   } is a functional operator that means the [[ixperiencitness]] produced by  the object with in the brackets.


Some terms deal with the actual objects others deal with properties of terms and still others deal with knowledge about the term or object or theocept.

'''Logical Operators'''

L1: <m>\supseteq </m>  this is the symbol for the logical operator  following symbols for the previous symbol can be exchanged in an equation with out changing the outcome

L2: <m>\cup </m>  this is the symbol for union

L3: <m> \cap </m>  this is the symbol for intersection

L4:   <m>\in </m>  this is the symbol for element of 

L5:  <m>\notin</m>   this is the symbol for not an element of 

L6:  <m>\exists</m>  this is the symbol for “there exists”

L7:  <m>\nexists </m> this is the symbol for “there does not exist”

L8:  <m>\forall </m>  this is the symbol meaning “for all”

L9:  <m>\uplus </m>  this is the symbol for concept union

L10: <m>\blacktriangleleft </m>  this is a elaboration of an equation operator it is used to restate an equation in a more detailed or longer form. For instance from number to name to designation to elaboration etc.

L10: <m>\blacktriangleright </m>  this is a reduction of an equation operator it is used to restate an equation in a shorter form. For instance from elaboration to designation to name to number etc.

L11:   " <m>\because</m> "   this is the symbol for inverse implication B “because” A

L12:   "<m> \therefore</m>" this is the symbol that means therefore.

L13:  <m>\supset  </m>  this is the symbol for implies or “if -- then --” if A then B


These following equations will be represented in two ways. The first line is a name and a simplified version of the equation. We call this first part the name or number of the equation. The second line or lines will be an elaboration of the equation. We call the second part the elaboration.

The reduced equation (the shortest form of the equation usually in the first line) will give information about the equation in a more simplified or shorted form. The first number before the period distinguishes the equation grouping. The second number indicated what the equation deals with in terms of [[originals]], [[idoriginals]], [[cidentireplicas]] etc. The third symbol or letter deals with the relational operator. The forth symbol or letter deals with the functional operator. The fifth section defines the variables in parenthesis that vary. Between the different sections can be periods.

The simplest reduction of an equation is a number as in equation “1”. It supplies little information. The next simplest reduction is a name like “citomultiplicity”. When equations relate to verbally defined concepts that have names, the equations will often be labeled with these names. The third level of reduction or elaboration is the simplest symbolic equation or SSE. The SSE through explicit rules allows for the elaboration of level four. The fourth level is where there is actually an equating symbols relating two or more things. Equations can be composed of different levels as long as there a clearly defined way of reducing or elaborating the different levels. There is no defined limit to the amount of elaboration that these equations can be submitted to. Eventually an elaboration can include very specific information about a concept or object.

There is a numbers attached to itoequations for the specific purpose of designating which type of itobody is being related 0 is for [[itoidentireplicas]], 1 for [[originals]], 2 for [[idoriginals]], 3 for [[coriginals]],  4 for [[cidentireplicas]],  5 for  [[videntireplicas]],  6 for [[fidentireplicas]], 7 for [[isoidentireplicas]], 8 for [[enhaidentireplicas]], 9 for [[musidentireplicas]], 10 for [[insidentireplicas]], 11 for [[tridentireplicas]], 12 for [[nrgidentireplicas]], 13 for [[comboidentireplicas]], 14 for [[simidentireplicas]],. So a beginning designation of (1.4)  on a itoequation would relate [[originals]]  and  [[cidentireplicas]]. "4.7" would relate [[cidentireplicas]] and [[isoidentireplicas]]. 

A number of simple redundant equations will be used to give a rudimentary working knowledge for this mathematics of consciousness before we come to the equations that the identity theory generates as principles and properties of consciousness in this universe.

==Simple Expressions==

<m>Ori(E)</m> This is the matter related properties of an original.

<m>Cito(U)</m> This is the universe that the [[cidentireplica]] is in. A different universe can have the same set of physical laws or any number of different physical laws than this universe has. It can also represent a different place and, or time in this universe where there are different physical laws as well that can effect the properties of the cidentireplica.  

<m>Ori(C,X)</m> This means the [[consciousness]] and [[ixperiencitness]]  or mentality of an [[original]].

<m>Ori(O,U,E,D,T,S,F)</m> this is a listing of physical  properties of an an original.

<m>Ori(O,U,E,D,T,S,F,B,C,X)</m> this is a listing of the physical and mental properties of an original.







== Simple Oriequations ==

[[Oriequations]] are equations that relate [[originals]] to each other, or to other types of [[itobodies]].



One of the simplest equations is:

<m> 1.1= \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}   Ori(O,U,E,D,T,S,F) == Ori(O,U,E,D,T,S,F)</m> 

Equation 1.1.= means that an originals is identical to itself when the two have the same identical original (O), Are in the same universe with the same universal physical laws (U), are made of the same matter/energy (E ), in the same dimensions/space (D), in the same time (T) , have identical structure (S),and functioning identically (F).

Equation 1.1= is a combination of the equations:

1. <m>1.1F   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =F= Ori(O,U,E,D,T,S,F)</m> 

This equations represent the idea that an original will function exactly like itself. This is a consequence and sub case of equation 1.1.=. This is also true because the functioning in one term is the same as the functioning in the other term: F = F.

2. <m>1.1M   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =M= Ori(O,U,E,D,T,S,F)</m> 

This sates that the mentality of the [[original]] is identical to the mentality of the original. If there is no mentality produced by the original the mentality produced is still the same, that of nothing.

3. <m>1.1S   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =S= Ori(O,U,E,D,T,S,F)</m> 

4. <m>1.1B   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =B= Ori(O,U,E,D,T,S,F)</m> 

It is hard to argue with the idea that a person will behave exactly like itself when all factors are the same. This is a consequence of Equation 1.1.F because identical functioning produces identical behavior, and a sub case of equation 1.1=. 

5. <m>1.1T   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =T= Ori(O,U,E,D,T,S,F)</m> 

6. <m>1.1D   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =D= Ori(O,U,E,D,T,S,F)</m> 

7. <m>1.1U   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =U= Ori(O,U,E,D,T,S,F)</m> 

8.  <m>1.1U   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F,C,X) =U= Ori(O,U,E,D,T,S,F,C,X)</m> 

Equation  <m>1.1=  \blacktriangleleft  [1.1.M, \uplus 1.1.B, \uplus 1.1.P, \uplus 1.1.N, \uplus, 1.1.O \uplus 1.1.U, \uplus 1.1.E, \uplus 1.1.D, \uplus 1.1.T, \uplus 11.S, \uplus 1.1.F]</m> 
 
This is just a statement of the definition of the relational operator ==.

Equations 1.1P, equation 1.1.N, equation 1.1.S etc. all fallow from equation 1.1.= by equation 1.1.=… 

<m> 1.1= \blacktriangleleft   Ori(O,U,E,D,T,S,C) == Ori(O,U,E,D,T,S,C)</m>

The symbol <m> \blacktriangleleft</m> means that an elaboration will follow in the next equation.The process of elaboration is important because it allows more information to be represented in an equation. 

<m> Ori(O,U,E,D,T,S,F) == Ori(O,U,E,D,T,S,F)  \blacktriangleright  1.1= .</m>

The symbol <m>\blacktriangleright</m> means that a reduction of the previous equation will follow in the next equation. The process of reduction or simplication is important because it allows one to see the bigger picture so to speak and it takes less space to represent it this way, and it is easier to manipulate.

==Simple Idoequations ==
 
[[Idoriginals]] are naturally occurring [[cidentireplicas]] of [[originals]]. Since they will occur naturally they are originals. And they are identical. They will be identified by the numeral 2 in the name of the equation.

<m>2.2=   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ido(O,U,E,D,T,S,F) == Ido(O,U,E,D,T,S,F)</m>  

An idoriginal is identical to itself in all ways.

<m>2.2M   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}      Ido(O,U,E,D,T,S,F) =M=  Ido(O,U,E,D,T,S,F)</m>  

This is a valid equation as well as <m>2.2.B,  2.2.P, 2.2.N, 2.2.S, 2.2.E,</m> etc. because they are subcases of  Equation 2.2.=.

<m> 2.2= \blacktriangleleft (2.2M, \uplus  2.2B, \uplus  2.2P, \uplus  2.2N, \uplus 2.2O, \uplus  2.2U, \uplus  2.2E , \uplus  2.2D, \uplus  2.2T , \uplus  2.2S , \uplus  2.2F)</m>   

When we combine equation including [[originals]] and identical originals we use the combination of  the numerals 1 representing originals and 2  representing idoriginals.

<m>1.2=   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}      Ori(O,U,E,D,T,S,F) ==  Ido(O,U,E,D,T,S,F)</m> 

This is true because of Equation 1.1= and PNI. All the subcases of this equation are valid as well. Such as 1.2M, 1.2B, 1.2D, 1.2S, 1.2T, etc. because of equation 1.2=…

Equation <m>1.2=\blacktriangleleft  [1.2M, \uplus 1.2B , \uplus 1.2P, \uplus 1.2/N, \uplus 1.2O, \uplus 1.2U, \uplus 1.2E , \uplus 1.2D , \uplus 1.2T, \uplus 1.2S , \uplus 1.2F]  </m>  

If we reverse the order of the equation, we have a new name and a different equation.

<m>2.1=   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ido(O,U,E,D,T,S,F,X) == Ori(O,U,E,D,T,S,F,X)</m>  

This equation is just as valid as Equation 1.2.=, As are all the subcases like Equation 2.1.M, Equation 2.1.P , etc.

1.2= …  2.1=     (1.2=)  …  (2.1=)

These identity equations are usually commutative so it does not matter if the [[Ori]], [[Ido]]  or [[Cito]] part comes first.  For example Cito(...) =m= Ori(...) will be the same as Ori(...) =m= Cito(...) . As a general rule we will start with the lowest numeral first but the reverse will be valid also.


'''The Principle of Name Interchangeability''' or  PNI is that the name of a object or concept can be changed without changing the concept of object.  If a term is being used as a name and not a functional operator and if renaming does not effect the concept or any aspect of the concept, renaming by another term is allowed. A term is used as a name and not a functional operator when the functional operator acts as a name and does not effect the terms it applies to in that situation. 

==Simple Citoequations==


Equation <m>1.4.=   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F,X) == Cito(O,U,E,D,T,S,F,X)</m> is an [[oriequation]] because it starts with a numeral  1 or "ori" in the elaboration.

The [[citoequation]] is actually written <m>4.1=   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}  Cito(O,U,E,D,T,S,F,X) == Ori(O,U,E,D,T,S,F,X)</m>

This both equation means the same thing just stated in reverse order.  what the equation means that  there is two different names for the same thing. This is because all of the factors in the parenthesis are the same. This follows from the equation 1.1=, and the principle of name replacement PNI.

Equation <m>4.1P   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Cito(O,U,E,D,T,S,F) =P= Ori(O,U,E,D,T,S,F)</m> 

They are physically identical because they are the same thing. They just have a different name. They are the same because their indices are the same. This follows from 1.1= and PNI. Or as a subcase of Equation 1.3= .

Equation <m>4.1M    \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Cito(O,U,E,D,T,S,F) =M= Ori(O,U,E,D,T,S,F)</m> 

This means that the actual material bodies are mentally identical. Again this may be viewed as a tautology because they are the same thing but with a different name. They are of the same original, in the same universe, are made of the same matter, in the same place, and time with exactly the same structure and functioning. If we wish to be precise, the meanings the concept of a Cid(... ) is different from the concept of a Ori(...). We have two different concepts applied to the same thing -- (O,U,E,D,T,S,C).

Equation <m>4.1F   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Cito(O,U,E,D,T,S,F) =F= Ori(O,U,E,D,T,S,F)</m> 

This equation is true when and because<m> Ori(F) ==Cid(F)</m>. This is correct because the functioning C is the same in both terms. In this case we have the same thing with a different name. It also follows from 1.1.F and principle of name interchangeability PNI. It also follows as a subcase of 1.4.=.

Equation <m>4.1B   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =B= Cito(O,U,E,D,T,S,F)</m> 

It is hard to argue with the idea that a person will act exactly like itself when all factors are the same except for its name Cito instead of Ori. This follows from equation  1.1.B and the principle of name interchangeability (PNI).

So far these  equations have been a little redundant because it defines exactly the same thing in each case. The only difference is in the names. These equations are valid and they begin to show the logic of this field of science and its mathematics.

In the following equations we will not always include the equations for the relationship between the original and idoriginal. They are essentially sub cases of the equations for the original and cidentireplica. 

Equation <m>  4.1= … [4.1M » 4.14 » 4.1P » 4.1/N » 4.1O » 4.1U » 4.1E » 4.1D » 4.1T » 4.1S » 4.1F]</m>
 
This is just a restatement of definition of 1.4.= in mathematical terms.

Equation 4.1=… states that if 1.4.= is valid then the equations <m>4.1M,1.4 B, 4.1P, 1.4N, 4.1O, 4.1U, 4.1E, 4.1D, 4.1T, 4.1S, and 4.1F</m> are valid as well. How is 4.1N valid when  <m>Ori(O,U,E,D,T,S,F) =N= Cito(O,U,E,D,T,S,F)</m> is not true? This is true because of the principle of name interchangeability.

Equation <m>13.31.=…     1.3.=… 3.1.=    </m>

<m>(1.3.= \supseteq 3.1.=) \supseteq (1.3.=) \supseteq (3.1.=)</m>


<m>13.31=\supseteq 1.2   (1.3.=\supseteq) \supseteq (3.1.=\supseteq)   </m> 

<m>{1.3= \supseteq [1.3.M » 1.3 B » 1.3.P » 1.3.N » 1.3.O » 1.3.U » 1.3.E » 1.3.D » 1.3.T » 1.3.S » 1.3.F]} \supseteq {3.1=\supseteq [3.1.M » 3.1 B » 3.1.P » 3.1.N » 3.1.O » 3.1.U » 3.1.E » 3.1.D » 3.1.T » 3.1.S » 3.1.F] }</m>

This is an equation that shows the associative principle in the nature of these equations.

Reduction of terms rules

Equation<m> 1.1=.F(F) F [Ori(O,U,E,D,T,S,F)]== Ori(F)</m>

<m>1.1F   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =P= Cito(O,U,E,D,T,S,F)</m> 

This equation states that the functioning of the original with all its terms is identical to the originals functioning.

Equation 1.1.F(C)  Ori(O,U,E,D,T,S,F) =F= Ori(F)
 
This equation says that the original with these terms (O,U,E,D,T,S,F)  is functionally identical to the originals functioning.

Other Equations of reduction

<m>1.1=.O(O), and1.1.O(O) corresponding to

<m>O[Ori(O,U,E,D,T,S,C)] == Ori(O) and 

<m>Ori(O,U,E,D,T,S,C) =O= Ori(O) respectively.

<m>1.1.=.U(U), and1.1.U(U)</m>
<m>1.1.=.D(D), and 1.1.D(D)</m>
<m>1.1.=.T(T), and 1.1.T(T)</m>
<m>1.1.=.S(S),  and 1.1.S(S)</m> 

Equations using functional operators

<m>1.1M1.2   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M{Ori(O,U,E,D,T,S,F)} =M= M{Ori(O,U,E,D,T,S,F)}</m> 

Equation 1.1.M1.2, means that the originals mentality, is mentality equal to it own mentality when the two have the same identical original (O), Are in the same universe with the same universal physical laws (U),are made of the same matter/energy (E ), in the same dimensions/space (D), in the same time (T) , have identical structure (S),and functioning identically (C) . In this case the superscript “1” in “1.2” represents one relational operator and the “2” represents 2 functional operators.

<m>1.2M1.2   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M{Ori(O,U,E,D,T,S,F)}  =M= M{Ido(O,U,E,D,T,S,F)} </m>

== Functional Equations ==

Equation 1.2.M1.2 means that an original’s mentality is mentally equal to the mentality of its idoriginal when the two have the same identical original (O), Are in the same universe with the same physical laws (U), are made of the same matter (E), in the same dimension/space (D), in the same time (T) , have identical structure (S), and functioning identically (C) . This is the same equation as above with a name replacement Ori instead of Ido.

Equation 1.4.M1.2    ﬁ

M{Ori (O,U,E,D,T,S,C ) } =M= M{Cid(O,U,E,D,T,S,C)}

<m>1.4\stackrel{M}{M}M  \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m> 

<m>1.4 {\overset{M}{M}M} \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m> 

<m>1.4 \sideset{_a^b}{_c^d}{M} \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>

<m>1.4\sideset{_a^b}{_c^d}M \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>

<m>1.4 \sideset{_a^b}{}{M} \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>

<m>1.4\sideset{_a^b}{}M \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>

<m>1.4 \sideset{_M^M}{}{M}\xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>

<m>1.4\sideset{_M^M}{_c^d}M \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>

<m>1.4M\_1^2\!\Omega_3^4 \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     M(Ori(O,U,E,D,T,S,F)) =M= M(Cito(O,U,E,D,T,S,F))</m>
 

Equation 1.3.M1.2 Means that the mentality of the cidentireplica is mentally equal to the mentality of the original when the two have the same identical original (O), exists in the same universe with the same physical laws (U), are made of the same matter (E), in the same dimension/space (D), in the same time (T), have identical structure (S), and are functioning identically (C) .  
  

<m>1.1\sideset{_2^F}{}{F}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     F[Ori(O,U,E,D,T,S,F)] =F= F[Ori(O,U,E,D,T,S,F)]</m>  

The functioning of the original is functionally equivalent to the functioning of the original. The F 1.2 in the equation designation means that there is one relational operator and two functional operators in the equation. If there are two relational operator in the equation then we represent it as  F 2..   F 3. for three relational operators. 

An example of more relational and functional operators in an equation is:

<m>1.1\sideset{_{3.4}^F}{}{F}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration} F[Ori(O,U,E,D,T,S,F)] =F= F[Ori(O,U,E,D,T,S,F)] =F= F[Ori(O,U,E,D,T,S,F)] =F= F[Ori(O,U,E,D,T,S,F)] </m> 

In this equation there are three relational operators and four functional operators

Equation 1.1.F(C)2    ﬁ   Ori(C) =F= Ori(C) 

<m>1.1\sideset{_{3.4}^F}{}{F}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     F[Ori(O,U,E,D,T,S,F)] =F= F[Ori(O,U,E,D,T,S,F)]</m>

<m>1.4F   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =P= Cito(O,U,E,D,T,S,F)</m> 


The originals functioning is functionally equivalent to the originals functioning.

This is correct because the functioning  C  is the same in both terms. The term (C)2 is used to represent the double use of C.  

Equation 1.1.F2(C)3    ﬁ  Ori(C) =F= Ori(C) =F= Ori(C)

In this equation there are two relational operators .F2 And three references to functioning (C)3. Equation 1.1.Fn(C)m extends this relationship to any number n, where m will be n + 1.

Equation 1.4.B1.1    ﬁ  B[Ori(O,U,E,D,T,S,F)] =B= Cito(O,U,E,D,T,S,F)

<m>1.4\sideset{_{1.1}^B}{}{B}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     B[Ori(O,U,E,D,T,S,F)] =B= Cito(O,U,E,D,T,S,F)</m>

This equation states that the behavior of the original is behaviorally identical to the cidentireplica. We use the superscript B1.1. To define that there is one relational operator =B= and one functional operator B[ ...] in the equation. 

Equation 1.4.B1.2.    ﬁ B[Ori(O,U,E,D,T,S,C)] =B= B[Cid(O,U,E,D,T,S,C)]

<m>1.4\sideset{_2^B}{}{B}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}    B[Ori(O,U,E,D,T,S,F)] =B= B[Cito(O,U,E,D,T,S,F)]</m>  

B1.2 means that there are one relational operator and two functional operators in this equation.

Equation 1.4.B1.F.2   

<m>1.4\sideset{_{2F}^B}{}{B}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     F[Ori(O,U,E,D,T,S,C)] =B= F[Cito(O,U,E,D,T,S,C)]</m>  


The functioning of the original is not the original or the behavior of the original.

This equation states that the functioning of the original is behaviorally equal to functioning of the cidentireplica. Technically since there is no behavior i.e., “the null behavior” and both sides have this null behavior so they are by default behaviorally equal.

Equation 1.4.=F.2    ﬁ   F[Ori(O,U,E,D,T,S,F)] == F[Cid(O,U,E,D,T,S,F)]

<m>1.4F   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E,D,T,S,F) =P= Cito(O,U,E,D,T,S,F)</m>  

This states that the functioning of the original is identical to the functioning of the cidentireplica. But the double equal sign also means identical in all other ways defined. Such as  =M=, =E= , etc. This is true because these other relational operators will be relating null or empty theocepts and thus will be  identical. 

1.3F…B     ﬁ
1.3.F …  1.3.B      ﬁ

Ori(O,U,E,D,T,S,F)] =F= Cito(O,U,E,D,T,S,F) … Ori(O,U,E,D,T,S,F)] =B= Cito(O,U,E,D,T,S,F)

This equation states that if the [[original]] and the [[cidentireplica]] are functionally identical then they will be behaviorally equal. In the case where there is not behavior produced it is true by default.

==Mixed Equations ==

<m>1.4\sideset{_{2F}^B}{}{B}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     F[Ori(O,U,E,D,T,S,C)] =B= F[Cito(O,U,E,D,T,S,C)]</m>  

New relational operators for equations

R14:  <m> =/=</m>   means not equal or identical, in one or more ways but not in all ways. We can put the slash sign in front of any relational operator for example;<m> =/B=,=/P=,=/M=, =/S=</m> etc. 

R15: <m>=//=</m>. This relational operator means the terms are not equal in all ways. 

For terms to be different there has to be a difference in the terms. To represent this difference we have added subscripts and superscripts to the terms, and to the terms in the names of the equations.

Equation 1.1./(E1m)    ﬁ    Ori(O,U,E1,D,T,S,C) =/= Ori(O,U,Em,D,T,S,C)

<m>1.1\sideset{}{_{1}^E}{=/=}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E_1,D,T,S,C) =/= Ori(O,U,E_m,D,T,S,C)</m>  

These are not identical because they are made of different matter. E1 does not equal Em .  Of course they are still in the same space and time, which can cause some problems, if this situation could actually occur. In this case we have the same name for two things that are different in one way. In reality the original could have been made of different matter.

Equation 1.1./P(E1m)    ﬁ  Ori(O,U,E1,D,T,S,C) =/P= Ori(O,U,Em,D,T,S,C)

<m>1.1\sideset{_{2F}^B}{}{B}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}    Ori(O,U,E_1,D,T,S,F) =/P= Ori(O,U,E_m,D,T,S,F)</m>  

The original is not physically equal to itself when it is made of different matter. The term E1m defines the change in matter from E1 to Em. E1 is fixed to 1 a specific grouping and arrangement of matter, but Em is a variable because m represents a variable. So Em represents any grouping or arrangement of matter that satisfies the other conditions (O,U,D,T,S,C).

Equation 1.4./(E1m)     ﬁ Ori(O,U,E1,D,T,S,C) =/= Cito(O,U,Em,D,T,S,C)

<m>1.4\sideset{}{_{1}^E}{=/=}    \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O,U,E_1,D,T,S,F) =/= Cito(O,U,E_m,D,T,S,F)</m>   

Like equation 1.1./(E1m) the cidentireplica and the original are not identical because they are not made of the same matter but they have the peculiar situation of being in the same place and at the same time. Whether this is physically possible is another question.

There are a number of equations that are not equivalent. There are how many equations using the relational operator =//=? 
In equation 1.4.// we do not need parenthesis because it includes all terms. But this equation is false because every term on both side of the equation is identical so they are equal.

1.4.//(1m)    ﬁ  Ori(O1,U1,E1,D1,T1,S1,C1) =//= Cito(Om,Um,Em,Dm,Tm,Sm,Cm)

<m>1.4\sideset{_{2F}^B}{}{B}   \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}     Ori(O_1,U_1,E_1,D_1,T_1,S_1,F_1) =//= Cito(O_m,U_m,E_m,D_m,T_m,S_m,F_m)</m>  


This equation will be valid because each term on different sides of the equation are different. (1m) represents all terms transposing from 1 in the original to m in the cidentireplica. However in this equation we cannot, by definition, call the [[cidentireplica]] a cidentireplica of this [[original]] because it is not identically functioning.

1.4.//(n m)    ﬁ  Ori(On,Un,En,Dn,Tn,Sn,Cn) =//= Cito(Om,Um,Em,Dm,Tm,Sm,Cm) 

What this equation states is that the original and the cidentireplica are not identical in any way defined by these terms.


1.3.//(1m)…  ﬁ
1.3.//(1m)…1.3./N(1m)    ﬁ

1.3.//(1m)  … 1.3./B(1m) » 1.3./M(1m) » 1.3./P(1m) » 1.3./N(1m) 1.3./S(1m) » 1.3./F(1m) » 1.3./O(1m) » 1.3./U(1m) » 1.3./E(1m) »
1.3./D(1m) » 1.3./T(1m) 
This equation can be elaborated again.

==Symbols for the construction of equation==

http://meta.wikimedia.org/wiki/Help:Formula, [[test]]

\sideset{_1^2}{_3^4}\prod_a^b	

<m>\sideset{_1^2}{_3^4}\prod_a^b</m> 

{}_1^2\!\Omega_3^4	

<m>{}_1^2\!\Omega_3^4</m> 

\overset{\alpha}{\omega}	

<m>\overset{\alpha}{\omega}	</m> 

\underset{\alpha}{\omega}

<m>\underset{\alpha}{\omega}</m> 	

\overset{\alpha}{\underset{\gamma}{\omega}}	

<m>\overset{\alpha}{\underset{\gamma}{\omega}}</m> 	

\stackrel{\alpha}{\omega}	

<m>\stackrel{\alpha}{\omega}</m> 

\forall \exists \empty \emptyset \varnothing	

<m>\forall \exists \empty \emptyset \varnothing	 </m>

\in \ni \not \in \notin \subset \subseteq \supset \supseteq	

<m>\in \ni \not \in \notin \subset \subseteq \supset \supseteq	 </m>

\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	

<m>\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	 </m>

\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup 	

<m>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup </m>	

<m> \blacktriangleleft  </m>

<m>     \blacktriangleright        </m>

\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq

<m> \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq</m>

\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq	

<m>\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq</m> 	

\sideset{_a^b}{_c^d}M

\sideset{_a^b}{_c^d}a

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