Discrete Mathematics: The Alphabet of the Digital World (Symbol Dictionary)
This dictionary is designed to help you understand how computers "think" and to enable you to read complex mathematical structures like a language. Each section is organized in a logical progression.
📌 Table of Contents
Section 1: Logic Gates (Intro to the Alphabet)
This is the decision-making mechanism of computer processors. Everything here is based on "True (1)" or "False (0)".
Symbol | Term | Absolute Law |
| NOT (Negation) | Flips the current state ( ). |
| AND (Conjunction) | Result is 1 ONLY if both sides are 1. |
| OR (Disjunction) | Result is 1 if at least one side is 1. |
| XOR (Exclusive Or) | Result is 1 if sides are different, 0 if they are the same. |
| Implies (If...then) | Result is 0 ONLY when  occurs. |
| Biconditional (If and only if) | Result is 1 ONLY if both sides have the same value. |
Section 2: The World of Numbers and Groups (Sets)
Defines how data is stored in "bags" and how they mix. This is the foundation of SQL database queries.
Symbol | Term | Absolute Law |
| Element of | States that an object strictly belongs to a group. |
| Union | Combines all distinct elements from two groups. |
| Intersection | Selects ONLY the "common" elements present in both groups. |
| Subset | When all members of one group are also inside another group. |
| Empty Set | Represents a "bag" with absolutely nothing inside. |
| Integers | The set of all whole numbers (negative, zero, and positive). |
Section 3: Quantity and Existence (Quantifiers)
The art of stating how many individuals a rule applies to. Used for setting strict constraints.
Symbol | Term | Absolute Law |
| For All (Universal) | Applies to everyone in the group without exception. |
| Exists (Existential) | True if you find at least one element that fits the rule. |
| Unique Existence | There is exactly and only one such element in the group. |
| Does Not Exist | States that no element can be found with the given property. |
| Therefore | Marks the final (conclusion) statement of a logical chain. |
Section 4: Connections and Probability (Graphs & Counting)
Shows how objects are connected and calculates the number of different options available.
Symbol | Term | Absolute Law |
| Factorial | Gives the total number of ways to arrange  distinct objects. |
| Summation (Sigma) | Adds up all numbers within a specific range. |
| Ceiling | Rounds a number up to the nearest integer. |
| Floor | Rounds a number down to the nearest integer. |
| Vertices (Nodes) | Represents the main points/junctions in a network (graph). |
| Edges | Represents the connections or paths between two points. |
Note: This dictionary serves as a guide for reading the language of Discrete Mathematics. Think of the symbols as words (verbs).
