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 *o* ∈ *A*. 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:

of the sets__Union__*A*and*B*, denoted*A*∪*B*, 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} .of the sets__Intersection__*A*and*B*, denoted*A*∩*B*, 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} .of__Set difference__*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*A*is sometimes used instead of^{c}*U*\*A*, particularly if*U*is a__universal set__as in the study of__Venn diagrams__.of sets__Symmetric difference__*A*and*B*, denoted*A*△*B*or*A*⊖*B*, 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, (*A*∪*B*) \ (*A*∩*B*) or (*A*

\*B*) ∪ (*B*\*A*).of__Cartesian product__*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)}.of a set__Power 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.