The limit of assumption is non-assumption, the limit of non-assumption is assumption, limit transcends assumption but allows it.
The limit of absence is presence; the limit of presence is absence; the limit of presence and absence is the contrast of each, the limit of the contrast of each is self-containment.
By degree a limit is a dualism for a limit is both seperation and connection, thus limit is a process;
by degree of being a dualism the limit is defined by the limit of non-dualism thus there is a dualism that contains both itself as dualism and its negation as gradation;
by degree of gradation limit is holographic as a grade of a limit is a limit, the gradation of limit is further limit thus limit is a process of itself.
There is limit;
Limit is relative to limit;
The relation is a limit;
The limit contains its own absence thus is generative;
The generation is self-contrasting inversion of limit and absence of limit;
The inversion of limit is the self-containment of limit by the limits of its absence and presence as limits within limits.
The self containment and self-contrast of limits are relative to eachother.
The relation of these limits are the limit as the presence and absence of itself.
A limit is both paradox and contradiction as generative limit.
Paradox and contradictions are limits, there contrast is a limit and there connection is a limit, limit contains limit.
The absence of a thing implies not only the opposite thing, its presence, but effectively infinite manner other things as the absence of a thing is the degree by which other things are limited by through the degree of what they are.
Absence is a negative limit.
The presence of a thing implies not only the opposite of the thing, its absence but effectively an infinite manner of other things by which it is not as the presence of a thing is the degree by which other things are limited by through the degree of what they are not.
Presence is a positive limit.
All limits are but the presence of one thing, as the presence of the many things which compose it, and the absence of other things, as the absence of the many things which contrast to it.
By degree limits are both presence and absence and as such are a paradox; paradox is the connection of opposites as one thing in harmony.
By degree limits are both presence and absence and as such are a contradiction; contradiction is the opposition of opposites as multiple things in tension.
Paradox and contradiction are the limit itself for by paradox is contradiction contained within the limit and by contradiction paradox is what allows the contrast of the limit;
a rational dualism of paradox and contradiction remains as the limit itself, with paradox and contradiction being the respective dualisms, each as themselves, while dually being a dualism as eachother.
The absence of absence is the simultaneous negation of absence and the continuity of it by ever further degree.
The presence of presence is the simultaneously inversion of presence into absence, by grades of presence, while these grades are the continuity of presence.
The absence of presence is but the gradation of it in one respect, as presence is minimized, while dually being the inversion of presence by degree of its self-contrast through absence.
The presence of absence is but the gradation of it in one respect, as absence magnifies, while dually being the inversion of absence by degree of its self-contrast through presence.
Absence is a self referential formalism that maintains duality and the dual aspect of gradation simultaneously; the duality of absence and absence of absence results in the gradation of both absence and absence of absence by degree of "absence of absence of absence" and "absence of absence of absence of absence". Each alternation is a relative grade of absence, relative to presence, while the dualism of absence and presence remains.
Absence: -
Absence of absence: --
****Inversion is repetition, the inversion rule is recursion that simultaneously results in self contrast and self containment as providing self-conditions. Where there is repetition there is inversion as self-contrast allows a limit to contain itself by its opposite; the completion of the sequence is its finite expression as limit is contained at all levels.
****The operators are the limits themselves, the limits are there own proof by degree of self-embedded pattern.
-
--
(--)-
(--)--
(--)--)-
Presence is a self referential formalism that maintains duality and the dual aspect of gradation simultaneously; the duality of presence and presence of presence results in the gradation of both presence and presence of presence by degree of "presence of presence of presence" and "presence of presence of presence of presence". Each alternation is a relative grade of presence, relative to absence, while the dualism of absence and presence remains.
Presence: +
Presence of presence: ++
****Inversion is repetition, the inversion rule is recursion that simultaneously results in self contrast and self containment as providing self-conditions. Where there is repetition there is inversion as self-contrast allows a limit to contain itself by its opposite;
The completion of the sequence is its finite expression as limit is contained at all levels.
****The operators are the limits themselves, the limits are there own proof by degree of self-embedded pattern.
+
++
(++)+
(++)++
(++)++)+
The recursion of absence contains absence at all levels, the recursion of presence contains presence at all levels. The recursion of absence inversely results in presence as the absence of the absence, the recursion of presence inversely results in absence by the presence of presence as grades; by recursion opposites invert into each other while providing a means of gradation for each through said inversion.
The distinction of opposites is a distinction of transparency by which one changes into another, by which one contrasts and the other occurs.
By absence there is the limit of absence: -
By the absence of absence there is the limit of absence as the presence: -- = +
By the absence of absence there is the continuation of absence through the limit of presence: (--)- = (+)-
By the continuation of absence through presence there is the presence of presence which results in the limit of absence: ++ = -
By the presence of presence there is the continuation of presence through the limit of absence: (++)+ = (+)-
By limit there is both presence and absence thus limit is process by means of inversion that generates each respectively.
The transformation boundary is each repetition of the limit as the limit is the means of transformation.
The repetition of limits is a limit thus limit is self-embedded as its own context.
Presence and absence can be used as limits, as they are limits, but any duality can be applied.
The calculus works for any dualism as a dualism is a limit containing limits. Absence can be replaced with X and presence replace with Y as all dualism are effectively an expression of presence and absence by degree of thetical and antithetical natures.
The absence of one presence is the presence of another.
The presence of one absence is the absence of another.
A calculus of limit can only have the single primitive of the limit itself as self relating. A formalism can have only X or only Y or only - or only + as argued above.
A true meta-formalism is a self contained operator as itself, no external requirement as necessary as such external requirements effectively are limits themselves thus nullifying the expansion of symbols.
Limit calculus can thus be observed as simply as the following:
●
●●
(●●)●
(●●)●●
(●●)●●)●
......
Which effectively reduces limit, in both form and function to autopoetic progress through recursive inversion. There is no assumption as assumption is subject to limit, there is no axiom as axiom is subject to limit, what remains is limit and the limit of the sequence of the limit. The limit is effectively not subject to being an assumed axiom as an assumed axiom is subject to being a limit by degree of contrast to the negation of assumed axiom.
Repetition is a limit, the inversion of what is repeated so that repetition may occur is the process of the limit.
● is indistinct limit, indistinct on its own terms; yet limit as containing all limits that reveal limit upon collapse. This is non-structure as infinite structures within and without, this is infinite structure within and without as non-structure.
●● is distinct limit self-contrasting that results in self-containment through self-context; by self contrast the limit observes the distinction of separation, as the space between the limits as a limit itself; by self containment the limit observes the distinction of connection. The limit is distinct by inversion of itself as “many”. This is dualism by degree of inversion of indistinct to distinct, this is gradation as the recursion of indistinction. This is structure; a structure is a set by degree of being a continuum through repetition. A structure is an identity by degree of repetition as symmetry; ●● is the expression of identity, conducive to A=A but transcendent as not only ● equal to ● but is effectively self-nesting thus resulting in the opposite of equality as self-containment that results in the inversion of indistinct to distinct, in these respects A=A and A=/=A, while dually A=/=-A and A=-A within a given context.
●● expresses four different logical degrees simultaneously:
*** ● contains itself thus A=A.
*** ● contrasts itself thus A=/=A
*** ● contains its own contrast thus A=-A
+++ ● contrasts its own containment thus A=/=-A
●● further expresses for different logical degrees simultaneously:
*** ● contains itself thus A and –A.
*** ● contrasts itself thus A or –A.
*** ● contains itself thus A and –A and A or –A.
*** ● contrasts itself thus A or –A or A and –A.
●● expresses six different mathematical/geometric degrees simultaneously:
*** ● is 0 or a 0d point.
*** ●● is the distinction of zero as 1, the distinction of a 0d point as 1 line segment.
*** ● through recursion results in both the number line and the line.
*** ●● through inversion results in line segments between line segments as negative spaces and negative numbers on the number line (when the positive and negative number lines are overlayed.
*** ●● results in positive numbers as additive and negative numbers as subtractive, thus number is embedded with arithmetic operators, number is effectively geometric space. The recursion of addition is mulitiplication, the recursion of multiplication is exponents (these are limits of connection); the recursion of subtraction is division, the recursion of division is roots (these are limits of separation). This represents both basic arithmetic and geometry.
+++ ●● results in a set as ● is a set contained within itself: each set is a variable as a variable, such as X is a set of numbers. This represents both sets and algebra.
●● Represents four degrees of consciousness:
*** ● is attention, attention is auto-poetic
*** ●● is attention on attention.
*** ●● is the perspective that contains attention as the recursive structure of attention.
*** ● is the transformation of reality by containment of attention through perspective as the inversion of perspective through attention by which said perspective transforms reality.
●● Represents four degrees of metaphysics:
*** ● represents the monad, non-dual, God, absolute unity.
*** ●● represents both dualism and gradation; both as emanation in western thought, illusion in eastern thought. It represents, monads, gods, absolute multiplicity.
+++ ● represents cause.
+++ ●● represents effect.
●● Represents four degrees of physics:
+++ ● Represents the quantum vacuum.
+++ ●● represent a field.
+++ ● represents an excitation/Particle
+++ ●● represents a wave.
●● Represents four degrees of measurement:
+++ ● represents a point of beginning/end.
+++ ●● represents the inversion of the point as a line.
+++ ●● represents the recursion of the point as a cycle.
+++ ● represents the superpositioning of forms
●● Represents four degrees of rationality.
+++ ● represents the assertion of which distinctions are structured upon.
+++ ●● represents the paradox as a unity of differences by self-containment as a dualism.
+++ ●● represents the contradiction as opposition of differences by self-contrast as a gradation.
+++ ● represents the dualism as a single distinction.
(●●)● is limit as self contrasting self-containment resulting in further recursion as the limit itself; the inversion of the indistinct limit into its opposite as distinct (●●) further inverts into being indistinct again ● thus resulting in an inversion. This is the inversion of structure to indistinction. This is dualism of structure and non-structure.
(●●)●● the inversion occurs further where now distinct limit is contained within distinct limit. This is the structure within structure. This is gradation of structures.
(●●)●●)● and the process continues as the limit itself where the repetition of the limit result in the inversion of being indistinct and distinct as the sequence itself, thus resulting in the limit of the sequence that is self-complete as ● occurs at all levels and ●● is self contained by ●. This is the structure within structure inverting to non-structure.
All limit can be expressed as the symbol ● thus effectively resulting in a calculus that describes all abstract and empirical assertions and observations that require the assertion of a limit. The symbol ● represents the foundation for any formalism as being the proto-logical meta-formalism for all formalisms.
● is the empty set that contains itself as ●● so that a set may occur.
● is the quantum vacuum by which self recursion results in excitations as particles and waves.
● is the 0d point by which recursion results in the geometric line.
● is 0 by which the quantification of 0 results in the limit of 1.
● is the Monad of Western Philosophy, the Non-Dual Void of Eastern Philosophy.
● is the point of awareness as attention itself in consciousness and meditative studies.
● is the beginning of any semantic assertion or axiom.
● is the foundation of unity and multiplicity relative to any form of measurement application.
● is the unconditional through which by recursion results in its own conditions.
● is the containment of paradox and contradiction as the distinction of paradox and contradiction
● is multivalent non-dualism
By repetition is a limit known as repetition results in symmetry as structure, by inversion is a limit known as inversion results in contrast that allows said symmetry to be structured, by the inversion of repetition are there various structures, by the repetition of inversion are there maintained structures.
The presence absence dichotomy of limit observes the foundational dualism of abstraction and empiricism as but other degrees as the presence of each is the relative absence of the other and yet each are limits contained within the limits of the dualism by which each are revealed as limits. Abstraction is a limit. Empiricism is a limit. Limit transcends both while containing both.
Existence is an autopoetic engine of limits, with this autopoetic engine being a limit.