SOME APPLICATIONS OF SIT-ELEMENTS TO SETS THEORY AND OTHERS

Sit – elements for continual sets Definition 2. The set of continual elements {а} = (а1, а2, . . . , аn) at one point x of space X we shall call Sit – element, and such a point in space is called holding capacity of the continual Sit – element. We shall denote Stx {a} . Definition3. The ordered continual self-consistency in itself as an element A of the first type is the ordered holding capacity containing itself as an element. Denote S1fA ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗ [3]. For example S∞ = sin∞ has such type. It denotes continual ordered selfconsistencies in itself as an element of next type—the range of simultaneous “activation” of numbers from [-1,1] in mutual directions: ↑ I ↓−1 1 . Also we consider next elements: S∞ =sin(-∞)--↓ I ↑−1 1 , T∞ = tg∞--↑ I ↓−∞ ∞ , T∞ =tg(-∞)--↓ I ↑−∞ ∞ , don’t confuse with values of these functions. Such elements can be summarized. For example: aS∞ +bS∞ =(a-b)S∞ + = (b − a) S∞ . Also may be considered operators for them. For


Definition3
. The ordered continual self-consistency in itself as an element A of the first type is the ordered holding capacity containing itself as an element. Denote 1 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ [3]. For example ∞ + = sin∞ has such type. It denotes continual ordered selfconsistencies in itself as an element of next type-the range of simultaneous "activation" of numbers from [-1,1] in mutual directions: ↑ I ↓ −1 1 . Also we consider next elements: ∞ − =sin(-∞)--↓ I ↑ −1 1 , ∞ + = tg∞--↑ I ↓ −∞ ∞ , ∞ − =tg(-∞)--↓ I ↑ −∞ ∞ , don't confuse with values of these functions. Such elements can be summarized. For example: a ∞ + +b ∞ − =(a-b) ∞ + = ( − ) ∞ − . Also may be considered operators for them. For example: f ∞ + (t-t0)={ ∞ + , = 0 0, ≠ 0 . All continual holding capacities in self-space are continual self-consistencies in itself as an element by definition. The continual self-consistencies in itself as an element may to appear as continual Sit-holding capacities and usual continual holding capacities. In these cases there is used usual measure and topology methods.

Connection of continual Sitelements with self-consistencies in itself as an element
Consider a third type of continual self-consistency in itself as an element. For example, based on х {а} , where {а} = (а 1 , а 2 , . . . , а ), i.e. n -continual elements at one point. It's possible to consider the continual self-consistency in itself as an element 3 with m continual elements and from {а}, at m<n, which is formed by the form (1) that is, only m continual elements are located in the structure х {а} .
Continual self-consistencies in itself as an element of the third type can be formed for any other structure, not necessarily Sit, only through the obligatory reduction in the number of continual elements in the structure. In particular, using the form (2) Structures more complex than S3f can be introduced.  ). There is the same for structures if it`s considereds as sets. Remark. We consider expression (*) where A is contained into B, R is expelled from Q. If A,B,D,C are taken in the capacities of sets, then we shall call (*) the dynamical hierarchical set of null type. Necessity of (*) arised for processes description in networks. Threshold element Sit -  [1]. May be considered more simple variant of dynamical set (**) where the set A is contained into the set B, or (***) A is expelled from B.
We consider the measure of external influence on b: **( ( ) )= A is usual group . We construct new mathematical objects constructively without formalism. The formalism by its contradiction may destroy this theory in accordance with Gödel's theorem on the incompleteness of any formal theory. But in next article we give back theory formalism properly: axioms and theorems proof. The activation of all networks enters it on self level at the activation. We introduce the concepts Cha -the measure of holding capacity and Cca-the cardinality of its contents. Cca coincides with cardinal number if contents of holding capacity is set. We consider compression powers of dynamical set: q1= answers I compression power of dynamical set A, q2= 1 -II compression power of dynamical set A,…, qn+1= -n+1 compression power of dynamical set A. We introduce the designations: CoQ-the contents of the holding capacity Q, Q ---empty holding capacity Q (without the contents).
≡ , as a result, there is a displacement from A to a higher level self: self-A. Axiom R1.ⱯB( =B). Axiom R2.ⱯB(ⱯB -1 ). St is also great for working with structures, for example: 1) --the structure A containment to B, where by B you can understand any capacity, other structure, etc, 2) --containment structure from Q into R. Similarly for displacement: 1) --displacement of structure A from B, 2) --displacement of the structure from Q to B. You can enter special operator Ct to work with structures: structures B with the structure of A, structures R with the structure from Q, unstructures B from the structure A, unstructures B from the structure which structures Q. Definition 1. A structure with a second degree of freedom will be called complete, i.e. "capable" of reversing itself with respect to any of its elements clearly, but not necessarily in known operators, it can form (create) new special operators (in particular, special functions).In particular, is such structure. Similarly for working with models, each of which is structured by its own structure, for example, use Sit-groups, Sit-rings, Sit-fields, Sit-spaces, self-groups, self-rings, self-fields, self-spaces. Like any task, this is also a structure of the appropriate capacity. Since the degree of freedom is doubly, it is clear that the structure of the equation contains a solution or structures the inversion of the equation with respect to unknowns, i.e. the structure of the equation is complete Self-H(self-hydrogen) , like other self-particles, does not exist in the ordinary, but in fact all self-molecules, self-atoms, self-particles are elements of the energy space.
Definition 5. Dynamical continual Sit-holding capacity with target weights {g1(t), g2(t )}: ( ) ( ) ( ) 2 ( ) ( ) 1 is called the process of a containment R(t) in Q(t) with relevant target weights. Definition 6. Dynamical continual holding capacity Q(t) with relevant target weights is called the process of a containment in Q(t) with relevant target weights.
Definition 7. Dynamical continual Sit-holding capacity ( ) ( ) ( ) 2 ( ) ( ) 1 with relevant target weights is called the process of a containment R(t) in Q(t) with relevant target weights. Definition 8. The dynamical containment of oneself continual A(t) of the first type is the process of putting A(t) into A(t). Denote 1 ( ) ( ).
Definition 9. The dynamical continual partial containment of oneself continual C(t) of the second type is the process of a containment of the continual program that allows C(t) to be generated. Let's denote 2 ( ) ( ). . Definition 10. Dynamical continual partial containment of oneself B(t) of the third type is the process of partial containment of continual B(t) into oneself or continual program that allows B(t) to be generated partially. Let us denote 3 ( ) ( ).

Connection of dynamical continual Sitelements with dynamical continual containment of oneself.
Consider a third type of dynamical continual partial containment of oneself. Dynamical containments of oneself of the third type can be formed for any other structure, not necessarily Sit, only through the obligatory reduction in the number of continual elements in the structure. In particular, using the form (2) [1].
Remark. Dynamical Sit-displacement of A(t) from B(t) will be denote through A(t) in oneself A(t) and dynamical expelling oneself A(t) out of oneself A(t). will be called anti-capacity from oneself. For example, "white hole" in physics is such simple anti-capacity. The concepts of "white hole" and "black hole" were formulated by the physicists proceeding from the physics subjects -usual energies level. The mathematics allows to find deeply and to formulate the concepts singular points in the Universe proceeding from levels of more thin energies. The experiments of Nobel laureates in 2022 year Asle Ahlen, Clauser John, Zeilinger Anton correspond to the concept of the Universe as its self-containment in itself. The connection between the elements of self-containment in itself is a property of self-containment in itself and therefore does not disappear when their location in it changes.The energy of selfcontainment in itself is closed on itself.
Hypothesis: the containment of the galaxy in oneself as spiral curl and the expelling her out of oneself defines its existence. A self-consistency in itself as an element A is the god of A, the self-consistency in itself as an element the globe-the god of the globe, the self-consistency in itself as an element man--the god of the man, the self-consistency in itself as an element of the universe--the god of the universe, the containment of A into oneself is spirit of A, the containment of the globe into oneself is is spirit of globe, the containment of the man into oneself is spirit of the man (soul), the containment of the universe into oneself is spirit of the universe. We may consider next axiom: any holding capacity is capacity of oneself in itself. This is for each energy capacity. The chinese book of Changes "I Ching" uses a structure similar to (*) implicitly. Supplement For an element from flora or fauna, one can try to consider the following energy distribution R=Q+D, Q-internal energy, D is the energy of its interaction with the external environment: --self-consistency in itself as an element for X1. More complex for implicit operator: F(X1,X2)=0. Then F(X1,X2)=0 F(X1,X2)=0 forms self-consistency in itself as an element for X1 relatively of X2 or for X2 relatively of X1. x obtains more power of the liberty and in this is direct decision (i.e. self-consistency in itself as an element for x ). Self-equation for x has its decision for x in direct kind. Self-task for x has its decision for x in direct kind. Self-question has its answer for x in direct kind. x acquires more degree of liberty and in this is direct decision. Supplement for Quantum Mechanics and through Sit-elements: Self-equation , ̂= exp(iH 0 t/ħ)ρexp(−iH 0 t/ħ), ́́= exp(iH 0 t/ ħ)Ŵ exp(−iH 0 t/ħ). Hamilton operator ̂=̂0 + W 0 , ̂0 -considered quantum system energy, consisting of two or more parts, without their interaction with each other, W 0 is the energy of their interaction, ρ-statistical operator [3]. Self-energy ̂= ̂0 + 0 0 + 0 =