1. Gnosticism and Fragmentation:

   • Gnosticism perceives reality as fragmented, where the material world is imperfect and separated from a higher spiritual realm.
   • We can metaphorically represent this using sets:
     • Define the universe set (U) to represent all existence: (U = \mathbb{R}) (where (\mathbb{R}) denotes the set of real numbers).
     • The broken parts are subsets of (U): (B_1, B_2, \ldots, B_n).
     • The reunion is the union of these subsets: (R = B_1 \cup B_2 \cup \ldots \cup B_n).

2. The Pleroma and Divine Aspects:

   • The Pleroma symbolizes the fullness of divine existence beyond our material world.
   • Let’s use sets to represent this:
     • Define the set (P) to represent the Pleroma: (P = {p_1, p_2, \ldots}) (where (p_i) are divine aspects).
     • The divine will, Logos, and Sophia are subsets of (P): (W \subseteq P), (L \subseteq P), and (S \subseteq P).

3. Perceptional Dualism and the Battle Within:

   • Gnosticism acknowledges the dualistic nature of existence.
   • Using set theory:
     • Define two disjoint sets: (L) (representing light) and (D) (representing darkness).
     • The battle within is the intersection of these sets: (B = L \cap D).

4. Theosis (Deification):

   • Theosis is central—a transformation that leads to union with the divine.
   • Metaphorically:
     • Define the set of humans: (H).
     • The set of deified beings: (D).
     • Theosis is the union of these sets: (T = H \cup D).

[ A \cup B = {x \mid x \in A \text{ or } x \in B} ]

In other words, it includes all elements that are in either set (A) or set (B), or both. If an element appears in both sets, it is still counted only once in the union.

1. (\subseteq) (Subset or Subset Equal):

   • This symbol represents the subset relationship between sets. If (A) is a subset of (B), we write (A \subseteq B). It means that every element in set (A) is also an element in set (B).
   • For example:
     • If (A = {1, 2}) and (B = {1, 2, 3}), then (A \subseteq B) because all elements of (A) are also in (B).

2. (\ldots) (Ellipsis):

   • The ellipsis ((\ldots)) indicates a continuation or repetition in a sequence. It is often used to represent an infinite sequence.
   • For example:
     • (1, 2, 3, \ldots) represents the natural numbers from 1 to infinity.

3. (\mathbb{R}) (Real Numbers):

   • (\mathbb{R}) represents the set of real numbers. Real numbers include all rational numbers (fractions) and irrational numbers (such as (\pi) or (\sqrt{2})).
   • For example:
     • (\mathbb{R} = {x \mid x \text{ is a real number}}).

1. (\mid) (Such That or Given):

   • The symbol (\mid) is used to specify a condition or property that elements in a set must satisfy.
   • For example:
     • If we have a set (A = {x \mid x > 0}), it means that (A) contains all positive real numbers.

2. (\text{B}):

   • The notation (\text{B}) represents a specific set or subset. It’s often used to label a set with a descriptive name.
   • For example:
     • If we define a set (B) as the set of even integers, we can write (B = {2, 4, 6, \ldots}).

3. (\cup) (Union):

   • The symbol (\cup) represents the union of sets. When we say (A \cup B), it means combining all elements from both sets (A) and (B) without any repetition.
   • Visually, it looks like this:
     • (A \cup B = {x \mid x \in A \text{ or } x \in B})
   • In other words, it includes all elements that are in either set (A) or set (B), or both. If an element appears in both sets, it is still counted only once in the union.uations,