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Introduction to Inequality Proofs

Introduction to Inequality Proofs

Inequality Proofs: Multiplication & Division of Inequalities

Inequality Proofs: Multiplication & Division of Inequalities

Inequality Proofs: A Fundamental Result

Inequality Proofs: A Fundamental Result

Inequality Proofs: Setting Out

Inequality Proofs: Setting Out

Proof by Contradiction (Example: Smallest Positive Rational Number)

Proof by Contradiction (Example: Smallest Positive Rational Number)

Proof by Contradiction: Arithmetic Mean & Geometric Mean

Proof by Contradiction: Arithmetic Mean & Geometric Mean

Four varieties of mathematical proof, illustrated

Four varieties of mathematical proof, illustrated

Proof: What is it, and how does it work?

Proof: What is it, and how does it work?

Different Algebraic Approaches to Proof

Different Algebraic Approaches to Proof

Exam Problem: Prove Inequality w/ Exponential & Linear Functions

Exam Problem: Prove Inequality w/ Exponential & Linear Functions

Interesting Inequality Proof w/ Inverse Trig (1 of 2: Calculus Proof)

Interesting Inequality Proof w/ Inverse Trig (1 of 2: Calculus Proof)

Interesting Inequality Proof w/ Inverse Trig (2 of 2: Davin's Sneaky Proof)

Interesting Inequality Proof w/ Inverse Trig (2 of 2: Davin's Sneaky Proof)

Double-Sided Inequality Proof

Double-Sided Inequality Proof

Inequality Proof: Summing Reciprocals of Squares (Experimental Silent Screencast)

Inequality Proof: Summing Reciprocals of Squares (Experimental Silent Screencast)

Inequality Proofs (1 of 5: Reciprocals, Adding & Multiplying Constants & Squaring and inequalities)

Inequality Proofs (1 of 5: Reciprocals, Adding & Multiplying Constants & Squaring and inequalities)

Inequality Proofs (2 of 5: Inequalities & Simultaneous chains, addition & multiplication)

Inequality Proofs (2 of 5: Inequalities & Simultaneous chains, addition & multiplication)

Inequality Proofs (3 of 5: Outline of three methods for proving inequalities)

Inequality Proofs (3 of 5: Outline of three methods for proving inequalities)

Inequality Proofs (4 of 5: Proving identity with properties & Intro to Proof by contradiction)

Inequality Proofs (4 of 5: Proving identity with properties & Intro to Proof by contradiction)

Inequality Proofs (5 of 5: Using Calculus to prove an inequality)

Inequality Proofs (5 of 5: Using Calculus to prove an inequality)

Harder Inequality Proofs (Using a graph and calculus to prove an inequality)

Harder Inequality Proofs (Using a graph and calculus to prove an inequality)

Inequality Proof - a² + 3b² + 5c² less than 1 (1 of 2: Algebraic Proof)

Inequality Proof - a² + 3b² + 5c² less than 1 (1 of 2: Algebraic Proof)

Inequality Proof - a² + 3b² + 5c² less than 1 (2 of 2: Visual Proof)

Inequality Proof - a² + 3b² + 5c² less than 1 (2 of 2: Visual Proof)

Inequality Proofs (Example 1 of 5: How many positive integer solutions?)

Inequality Proofs (Example 1 of 5: How many positive integer solutions?)

Inequality Proofs (Example 2 of 5: Which number is largest?)

Inequality Proofs (Example 2 of 5: Which number is largest?)

Inequality Proofs (Example 3 of 5: Is 2^300 bigger or 3^200?)

Inequality Proofs (Example 3 of 5: Is 2^300 bigger or 3^200?)

Inequality Proofs (Example 4 of 5: Arithmetic & Geometric Means)

Inequality Proofs (Example 4 of 5: Arithmetic & Geometric Means)

Inequality Proofs (Example 5 of 5: Investigating a large product)

Inequality Proofs (Example 5 of 5: Investigating a large product)

Proof by Contradiction (1 of 2: How does it work?)

Proof by Contradiction (1 of 2: How does it work?)

Proof by Contradiction (2 of 2: Infinite primes)

Proof by Contradiction (2 of 2: Infinite primes)

Introduction to the Nature of Proof (1 of 3: Prologue)

Introduction to the Nature of Proof (1 of 3: Prologue)

Introduction to the Nature of Proof (2 of 3: Building blocks)

Introduction to the Nature of Proof (2 of 3: Building blocks)

Introduction to the Nature of Proof (3 of 3: Liars & truth-tellers)

Introduction to the Nature of Proof (3 of 3: Liars & truth-tellers)

Foundations of Proof (1 of 2: Statements, implications, negations)

Foundations of Proof (1 of 2: Statements, implications, negations)

Foundations of Proof (2 of 2: Equivalence & quantifiers)

Foundations of Proof (2 of 2: Equivalence & quantifiers)

Negating Compound Statements (1 of 2: Reviewing the basics)

Negating Compound Statements (1 of 2: Reviewing the basics)

Negating Compound Statements (2 of 2: And, Or, Quantifiers)

Negating Compound Statements (2 of 2: And, Or, Quantifiers)

Implications & Contrapositives (1 of 2: How do they relate?)

Implications & Contrapositives (1 of 2: How do they relate?)

Implications & Contrapositives (2 of 2: Further examples)

Implications & Contrapositives (2 of 2: Further examples)

Proof: a³ - a is always divisible by 6 (1 of 2: Two different approaches)

Proof: a³ - a is always divisible by 6 (1 of 2: Two different approaches)

Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)

Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)

Proof by Contraposition

Proof by Contraposition

Proof by Contradiction: log₂5 is irrational

Proof by Contradiction: log₂5 is irrational

Proof - Odd composite numbers (1 of 3: Setup)

Proof - Odd composite numbers (1 of 3: Setup)

Proof - Odd composite numbers (2 of 3: Understanding the negation)

Proof - Odd composite numbers (2 of 3: Understanding the negation)

Proof - Odd composite numbers (3 of 3: By contradiction)

Proof - Odd composite numbers (3 of 3: By contradiction)

Proving Algebraic Inequalities (1 of 3: Introductory principles)

Proving Algebraic Inequalities (1 of 3: Introductory principles)

Proving Algebraic Inequalities (2 of 3: Using the sign)

Proving Algebraic Inequalities (2 of 3: Using the sign)

Proving Algebraic Inequalities (3 of 3: Further strategies)

Proving Algebraic Inequalities (3 of 3: Further strategies)

Proof: √3 + √2 is irrational

Proof: √3 + √2 is irrational

Proof: Mersenne primes

Proof: Mersenne primes

Divisibility Proof (1 of 2: Sum of 7 consecutive integers)

Divisibility Proof (1 of 2: Sum of 7 consecutive integers)

Divisibility Proof (2 of 2: Using algebraic expansion)

Divisibility Proof (2 of 2: Using algebraic expansion)

How many subsets in a set? (1 of 2: Induction proof)

How many subsets in a set? (1 of 2: Induction proof)

How many subsets in a set? (2 of 2: Combinatorial proof)

How many subsets in a set? (2 of 2: Combinatorial proof)

Irrational Logarithm Proof (2 of 2: By graphing)

Irrational Logarithm Proof (2 of 2: By graphing)

Irrational Logarithm Proof (1 of 2: By cases)

Irrational Logarithm Proof (1 of 2: By cases)

Inequality Proof - Fraction Sum (3 of 3: Applying calculus)

Inequality Proof - Fraction Sum (3 of 3: Applying calculus)

Inequality Proof - Fraction Sum (2 of 3: Graphical representation)

Inequality Proof - Fraction Sum (2 of 3: Graphical representation)

Inequality Proof - Fraction Sum (1 of 3: Algebraic approach)

Inequality Proof - Fraction Sum (1 of 3: Algebraic approach)

Why are the prime rows in Pascal's Triangle so special?

Why are the prime rows in Pascal's Triangle so special?

Proving a Converse Statement (3 of 3: Using the inverse)

Proving a Converse Statement (3 of 3: Using the inverse)

Proving a Converse Statement (2 of 3: Considering the contrapositive)

Proving a Converse Statement (2 of 3: Considering the contrapositive)

Proving a Converse Statement (1 of 3: Investigating original proposition)

Proving a Converse Statement (1 of 3: Investigating original proposition)

Grid Painting Question (2 of 2: Generalising the result)

Grid Painting Question (2 of 2: Generalising the result)

Grid Painting Question (1 of 2: Establishing a base case)

Grid Painting Question (1 of 2: Establishing a base case)

Inequality proof: average of squares vs. square of average

Inequality proof: average of squares vs. square of average