The Science of it All

What is SET theory and why!

set_theory

Briefly, SET theory is a perfect example of obfuscation (transitive
and intransitive verb to make something obscure or unclear, especially by making it unnecessarily complicated) done by scientists and politicians.

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be
collected into a set, set theory is applied most often to objects that are relevant to mathematics. Seems pretty straightforward doesn’t it? But because this is mathematics they have to complicate it or it wouldn’t be scientific. So they created an entire language to deal
with sets of objects. Set theory begins with a fundamental binary relation between an object o and a set A. If o is a member
(or element) of A, write oA. Since sets are objects, the membership relation can relate sets as well.

Just as arithmetic features binary operations on numbers, set
theory features binary operations on sets. The:

  • Union of the sets A and B, denoted AB, is the set of all objects that are a member of A, or B, or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} .
  • Intersection of the sets A and B, denoted AB, is the set of all objects that are members of both A and B. The
    intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3} .
  • Set difference of U and A, denoted U \ A, is the set of all members of U that are not members of A. The set difference {1,2,3} \ {2,3,4} is {1} , while, conversely, the set difference {2,3,4} \ {1,2,3} is {4} . When A is a subset of U, the set difference U \ A is also called the complement
    of A in U. In this case, if the choice of U is clear
    from the context, the notation Ac is sometimes used instead of U \ A, particularly if U is a universal set as in the study of Venn diagrams.
  • Symmetric difference of sets A and B, denoted AB or AB, is the set of all objects that are a member of exactly one of A and B (elements which are in one of the sets, but not in both). For instance, for the sets {1,2,3} and {2,3,4} , the
    symmetric difference set is {1,4} . It is the set difference of the union and the intersection, (AB) \ (AB) or (A
    \ B) ∪ (B \ A).
  • Cartesian product of A and B, denoted A × B, is the set whose members are all possible ordered pairs (a,b) where a is a member of A and b is a member of B. The cartesian product of {1, 2} and {red, white} is {(1, red), (1, white), (2, red), (2, white)}.
  • Power set of a set A is the set whose members are all possible subsets of A. For example, the power set of {1, 2} is { {}, {1}, {2}, {1,2} } .

Some basic sets of central importance are the empty set (the unique set containing no elements), the set of natural numbers, and the set of real numbers. (As opposed to “fake numbers”? )

Not only that but they’ve come up with this: fuzzy set theory is an object that has a degree of membership in a set, a number between 0 and 1. For example, the degree of membership of a person in the set of “tall people” is more flexible than a simple yes or no answer and can be a real number such as 0.75.

K.I.S.S. (Keep It Stupid Simpleton) Now, I’m not totally opposed to everything I have used fuzzy logic in the development of software program’s. For our purposes we just need to keep it simple – when we talk about sets it’s either an idea or an object is part of or not part of that set.

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