This is a hub for learning how to mathematically prove statements or equations are true. The best way to learn through this hub is to ensure you know the assumed knowledge, and learn in order from left to right, up to down. If you are learning alongside a class/textbook, use this hub as a reference if you get confused about a topic. > [!bug]- Assumed Knowledge The following list is of concepts that are assumed you know, and are directly referenced in one or more topics. > - [[Even & Odd Numbers]] > - Classifying numbers as even and odd > - [[Integers|Integer]] > - A way of describing whole numbers > - [[Irrational Numbers]] > - Numbers that can't be written as fractions > - [[Natural Numbers]] > - Whole only positive numbers > - [[Whole Number]] > - Natural numbers, including 0 > - [[Greatest Common Divisor (gcd)]] > - The largest number that divides evenly # Logic - [[Propositions|1. Propositions]] - Complete statements that are true or false - [[Predicates|2. Predicates]] - Statements with variables that determine the truth value - [[Conjunction|3. Conjunction]] - Logical "AND" for joining two statements - [[Negation|4. Negation]] - Logical "NOT" for flipping the truth - [[Conditional Statements|5. Conditional Statements]] - If, then statements # Proofing Methods - [[Direct Proof|1. Direct Proof]] - Showing a statement is true from definitions - [[Proof by Contradiction (Indirect Proof)|2. Indirect Proof]] - Showing a statement's conclusion is false, thus the statement is false - [[Proof by Contraposition|3. Proof by Contraposition]] - Assume the opposite and reach a contradiction - [[Mathematical Induction|4. Mathematical Induction]] - Prove by showing it holds for 1 and showing it its true for n, like a ladder - [[Algebraic Proof|5. Algebraic Proof]] - Proof using algebraic definitions - [[Combinatorial Proof|6. Combinatorial Proof]] - Proof using counting definitions