Set Theory – Paisley’s Law
Set theory is a branch of mathematics that studies collections of objects, called sets. These objects, or elements, can be anything, but in mathematics, they are often numbers, functions, or even other sets. Set theory provides a foundational language for describing mathematical concepts and is used extensively in other areas of mathematics like algebra, analysis, and topology according to Let’s Talk Science.
Key Concepts:
Complement: The complement of a set A (within a universal set U), denoted by A’, contains all elements in U that are not in A.
Sets: A set is a well-defined collection of distinct objects, called elements. Sets are typically denoted by curly braces { }.
Elements: The objects within a set are called its elements or members.
Membership: The notation “a ∈ A” means that “a” is an element of set A.
Subsets: If all elements of set A are also elements of set B, then A is a subset of B, denoted as A ⊆ B.
Proper Subsets: If A is a subset of B, but A is not equal to B, then A is a proper subset of B, denoted as A ⊂ B.
Universal Set: The set containing all possible elements under consideration is called the universal set, often denoted by U.
Empty Set: The set with no elements is called the empty set, denoted by {} or ∅.
Set Operations: Common operations on sets include:
Union (∪): The union of two sets A and B, A ∪ B, contains all elements that are in A or B (or both).
Intersection (∩): The intersection of two sets A and B, A ∩ B, contains all elements that are in both A and B.
Examples:
The intersection of the set of even numbers and the set of prime numbers is {2}.
{1, 2, 3} is a set containing the numbers 1, 2, and 3.
{red, green, blue} is a set of colors.
White = U (the Universal set of all possible spectra)
The set of all even numbers is an example of an infinite set.
Why is set theory important?
- Foundation of Mathematics:Set theory provides a foundation for all of mathematics. It allows mathematicians to define and reason about all other mathematical objects.
- Precise Language:Set theory provides a precise and unambiguous language for describing mathematical concepts, which is crucial for developing and understanding complex mathematical theories.
- Applications: While set theory is primarily a foundational tool, it has applications in various fields, including computer science, logic, and even areas like music theory (musical set theory).
This video provides an overview of set theory, including types of sets, unions, and intersections:
In-Numerology: Paisley Sequence Framework (PSF)
Order Through In-Numerology
The complex system of numbers in numbers, we call it in-numerology, is a good discipline for understanding the meaning of numeric relationships and ratios. As we seek to understand the ever-changing moments around us, in-numerology reveals the natural way our Light communicates through photonic light signature patterns. These patterns articulate quantifiable ratios linked to all the interconnected stages of mitotic creation; from the first thought(future) to the pre-present(pregnancy) to the materialized present ‘Now’ instance, to stored past memory. Over three years of research using in-numerology has validated that all SOL numbers resonate harmonically. Based on this diligence, the PSF is shared as a solely holistic framework that unifies disparate numeric ‘dialects’ within one native mother tongue . It will continue to be tested and spiritually reflected upon, scientifically calibrated, etc. The more precise our numbers the better the outcomes for healing and system self-repair (error-correcting).
Numerology
https://www.sacredgeometryshop.com/sacred-geometry/sacred-geometry-numerology
23.4º DIFFERENCE BETWEEN TROPICAL VS. SIDEREAL ZODIAC
This difference mirrors the measurement variances we have retraced between the rational planetary structures and universal celestial alignments, reiterating that an impact shifted our planetary system. Think of rotating two complementary components back into their original position–matching pairs of rational and celestial signal stream coordinates. These error corrections are addressed throughout this reintroduction to our Divine Source Light Technology.
Gematria
Gematria is the cipher revealing the alpha numeric correspondence aligned with our natural light language.
(/ɡəˈmeɪtriə/; Hebrew: גמטריא or גימטריה, gimatria, plural גמטראות or גימטריות, gimatriot)[1] is the practice of assigning a numerical value to a name, word, or phrase by reading it as a number, or sometimes by using an alphanumeric cipher. The letters of the alphabets involved have standard numerical values, but a word can yield several values if a cipher is used.
The first documented use of gematria is from an Assyrian inscription dating to the 8th century BCE, commissioned by Sargon II. In this inscription, Sargon II states: “the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name.”[9]
Other Disciplines
1. Category Theory:
- Abstraction and Generalization: Category Theory provides a higher level of abstraction than set theory, allowing mathematicians to study structures and relationships between them in a more general way.
- Foundational Role: It can serve as a foundation for various mathematical fields, including algebra, geometry, and topology.
- Focus on Structures: Category theory emphasizes the relationships between mathematical objects rather than the objects themselves, making it useful for unifying different areas of mathematics.
2. Model Theory:
- Relationship between Structures and Logic: Model theory investigates the relationship between mathematical structures and the formal languages used to describe them.
- Study of Definable Sets: It explores the sets that can be defined within a given mathematical structure and how these sets relate to each other.
- Connections to Logic: Model theory has strong ties to mathematical logic, particularly in understanding the consistency and completeness of formal systems.
3. Mereology:
Mereology can be seen as a complementary theory to set theory, providing a different perspective on structure and composition.
Mereology studies the relationships between parts and wholes.
It focuses on how objects can be composed of other objects, rather than simply grouping them into sets.