Канал: Every Other Odd

(5.5.9) Proving Correctness with Loop Invariants

(5.5.9) Proving Correctness with Loop Invariants

(5.5.5) Proving Predicate Invariance in a While Loop

(5.5.5) Proving Predicate Invariance in a While Loop

(5.5.1) Proving Predicate Invariance in a While Loop

(5.5.1) Proving Predicate Invariance in a While Loop

(5.4.37) Proving the Well-Ordering Principle Using Ordinary Induction

(5.4.37) Proving the Well-Ordering Principle Using Ordinary Induction

(5.4.33) Proving Ordinary Mathematical Induction from Strong Induction

(5.4.33) Proving Ordinary Mathematical Induction from Strong Induction

(5.4.29) Proving Existence of Integer Bounds on Rational Numbers Using Well-Ordering Principle

(5.4.29) Proving Existence of Integer Bounds on Rational Numbers Using Well-Ordering Principle

(5.4.25) Flawed Proof That All Powers of Nonzero Real Numbers Equal 1

(5.4.25) Flawed Proof That All Powers of Nonzero Real Numbers Equal 1

(5.4.21) Strong Induction Proof of Recursive Sequence Using Floor and Ceiling Functions

(5.4.21) Strong Induction Proof of Recursive Sequence Using Floor and Ceiling Functions

(5.4.17) Units Digit Pattern in Powers of 4

(5.4.17) Units Digit Pattern in Powers of 4

(5.4.13) Strong Mathematical Induction: Unique Factorization of Integers

(5.4.13) Strong Mathematical Induction: Unique Factorization of Integers

(5.4.9) Strong Mathematical Induction: Proving an Upper Bound on the Lucas Sequence

(5.4.9) Strong Mathematical Induction: Proving an Upper Bound on the Lucas Sequence

(5.4.5) Inductive Proof Technique for a Recursive Sequence Formula

(5.4.5) Inductive Proof Technique for a Recursive Sequence Formula

(5.4.1) Proving All Terms in a Recursive Sequence are Odd with Strong Induction

(5.4.1) Proving All Terms in a Recursive Sequence are Odd with Strong Induction

(5.3.45) Identifying Mistakes in Mathematical Induction Proofs

(5.3.45) Identifying Mistakes in Mathematical Induction Proofs

(5.3.41) Proving a Unique Messaging Pattern in a Group of People

(5.3.41) Proving a Unique Messaging Pattern in a Group of People

(5.3.37) Proving a Sum on a Circular Disc with Integers 1-30

(5.3.37) Proving a Sum on a Circular Disc with Integers 1-30

(5.3.33) Solving the 4x6 Checkerboard Puzzle with L-shaped Traminos

(5.3.33) Solving the 4x6 Checkerboard Puzzle with L-shaped Traminos

(5.4.29) Proving Even Number of Bs in Strings Using Mathematical Induction

(5.4.29) Proving Even Number of Bs in Strings Using Mathematical Induction

(5.3.25) Proving Sequence Growth Exceeds 4n with Mathematical Induction

(5.3.25) Proving Sequence Growth Exceeds 4n with Mathematical Induction

(5.3.21) Mathematical Induction Proof: Comparing Square Root of n and a Sum Series

(5.3.21) Mathematical Induction Proof: Comparing Square Root of n and a Sum Series

(5.3.17) Proving an Inequality Using Mathematical Induction: A Step-by-Step Guide

(5.3.17) Proving an Inequality Using Mathematical Induction: A Step-by-Step Guide

(5.3.13) Proving Divisibility by x-y for Powers of x and y Using Mathematical Induction

(5.3.13) Proving Divisibility by x-y for Powers of x and y Using Mathematical Induction

(5.3.9) Proving Divisibility by 6 for Powers of 7 Using Mathematical Induction

(5.3.9) Proving Divisibility by 6 for Powers of 7 Using Mathematical Induction

(5.3.5) How to Prove Inequalities with Mathematical Induction for Positive Integers

(5.3.5) How to Prove Inequalities with Mathematical Induction for Positive Integers

(5.3.1) Mathematical Induction: Proving Money Compositions with 3¢ and 8¢ Coins

(5.3.1) Mathematical Induction: Proving Money Compositions with 3¢ and 8¢ Coins

(5.1.13) Exploring Sequences: Finding Explicit Formulas for Fractional Patterns

(5.1.13) Exploring Sequences: Finding Explicit Formulas for Fractional Patterns

(5.2.40) Proving Divisibility of a Sum of Squares by a Prime Number (BONUS)

(5.2.40) Proving Divisibility of a Sum of Squares by a Prime Number (BONUS)

(5.2.37) Identifying and Correcting Errors in Inductive Proof Fragments

(5.2.37) Identifying and Correcting Errors in Inductive Proof Fragments

(5.2.33) Deriving a Closed-Form Formula for an Arithmetic Series

(5.2.33) Deriving a Closed-Form Formula for an Arithmetic Series

(5.2.29) Deciphering an Alternating Geometric Series: From Summation to Closed Form

(5.2.29) Deciphering an Alternating Geometric Series: From Summation to Closed Form

(5.2.25) Breaking Down Geometric Series: From Basic Summation to Complex Forms

(5.2.25) Breaking Down Geometric Series: From Basic Summation to Complex Forms

(5.2.21) Evaluating Sums: Formulaic Approach vs. Ingenious Method

(5.2.21) Evaluating Sums: Formulaic Approach vs. Ingenious Method

(5.2.17) Mathematical Induction Proof for a Product Involving Powers

(5.2.17) Mathematical Induction Proof for a Product Involving Powers

(5.2.13) Inductive Proof of a Summation Involving Products of Consecutive Numbers

(5.2.13) Inductive Proof of a Summation Involving Products of Consecutive Numbers

(5.2.9) Inductive Proof of a Summation Formula Involving Powers of Four

(5.2.9) Inductive Proof of a Summation Formula Involving Powers of Four

(5.2.5) Step-by-Step Guide to Proving an Inductive Mathematical Statement

(5.2.5) Step-by-Step Guide to Proving an Inductive Mathematical Statement

(5.2.1) Exploring the Inductive Step: Generalizing Inductive Reasoning Using Examples

(5.2.1) Exploring the Inductive Step: Generalizing Inductive Reasoning Using Examples

(5.1.89) Converting Decimal to Hexadecimal By Repeated Division by 16 via Modified Algorithm

(5.1.89) Converting Decimal to Hexadecimal By Repeated Division by 16 via Modified Algorithm

(5.1.85) Tracing Algorithm 5.1.1 to Convert Base-10 to Base-2

(5.1.85) Tracing Algorithm 5.1.1 to Convert Base-10 to Base-2

(5.1.81) Converting Integers from Base 10 to Base 2 Using Repeated Division

(5.1.81) Converting Integers from Base 10 to Base 2 Using Repeated Division

(5.1.77) Proving n! + 2 is divisible by 2 and and n! + k is divisible by k for n ≥ 2

(5.1.77) Proving n! + 2 is divisible by 2 and and n! + k is divisible by k for n ≥ 2

(5.1.73) Calculating Combinations: Understanding 3 Choose 0

(5.1.73) Calculating Combinations: Understanding 3 Choose 0

(5.1.69) Simplifying Factorial Expressions: n! Over (n-k)!

(5.1.69) Simplifying Factorial Expressions: n! Over (n-k)!

(5.1.65) Simplifying n!/(n-1)!

(5.1.65) Simplifying n!/(n-1)!

(5.1.61) Combining Products into a Single Product Expression

(5.1.61) Combining Products into a Single Product Expression

(5.1.57) Summation Index Variable Transformation: Shifting from 'i' to 'j'

(5.1.57) Summation Index Variable Transformation: Shifting from 'i' to 'j'

(5.1.53) Change of Variable in Summation Notation: From 'k' to 'i'

(5.1.53) Change of Variable in Summation Notation: From 'k' to 'i'

(5.1.49) Transforming Series into Summation Notation

(5.1.49) Transforming Series into Summation Notation

(5.1.45) Converting Expressions into Product Notation

(5.1.45) Converting Expressions into Product Notation

(5.1.41) Separating the Final Term: Breaking Down Summations

(5.1.41) Separating the Final Term: Breaking Down Summations

(5.1.37) Understanding Single Summation Expressions: From Expanded to Summation Form

(5.1.37) Understanding Single Summation Expressions: From Expanded to Summation Form

(5.1.33) Navigating Summations: Evaluating Series for Specific Variable Values

(5.1.33) Navigating Summations: Evaluating Series for Specific Variable Values

(5.1.29) Decoding Geometric Series: Writing Summations in Expanded Form

(5.1.29) Decoding Geometric Series: Writing Summations in Expanded Form

(5.1.25) Unpacking Products: Connecting Math Computation to Iterative Processes #discretemath

(5.1.25) Unpacking Products: Connecting Math Computation to Iterative Processes #discretemath

(5.1.21) Breaking Down Summations: From Math Concept to Programming Logic

(5.1.21) Breaking Down Summations: From Math Concept to Programming Logic

(5.1.17) Crafting an Alternative Formula Using the Floor Function

(5.1.17) Crafting an Alternative Formula Using the Floor Function

(5.1.9) Delving into the Logarithmic Sequence: Computation and Behavior

(5.1.9) Delving into the Logarithmic Sequence: Computation and Behavior

(5.1.5) Deriving the First Four Terms of a Sequence Using the Floor Function Formula

(5.1.5) Deriving the First Four Terms of a Sequence Using the Floor Function Formula

(5.1.1) Determining the First Four Terms of a Sequence Defined by a Given Formula

(5.1.1) Determining the First Four Terms of a Sequence Defined by a Given Formula

(4.10.29) Mathematical Proof: Relationship Between GCD and LCM

(4.10.29) Mathematical Proof: Relationship Between GCD and LCM

(4.10.25) Mathematical Proof and Algorithm Modification

(4.10.25) Mathematical Proof and Algorithm Modification

(4.10.21) Algorithm Analysis: Determining Whether Integers Are Relatively Prime

(4.10.21) Algorithm Analysis: Determining Whether Integers Are Relatively Prime

(4.10.17) Algorithm Tracing: Using the Euclidean Algorithm to Find the Greatest Common Divisor

(4.10.17) Algorithm Tracing: Using the Euclidean Algorithm to Find the Greatest Common Divisor

(4.10.13) Calculating the Greatest Common Divisor Using the Euclidean Algorithm

(4.10.13) Calculating the Greatest Common Divisor Using the Euclidean Algorithm

(4.10.9) Finding the Greatest Common Divisor of 27 and 72 Using the Euclidean Algorithm

(4.10.9) Finding the Greatest Common Divisor of 27 and 72 Using the Euclidean Algorithm

(4.10.5) Calculating the Values of E and F After Execution of Loops in 4 and 5

(4.10.5) Calculating the Values of E and F After Execution of Loops in 4 and 5

(4.10.1) Algorithm Analysis: Tracking Variable Values Through Program Execution

(4.10.1) Algorithm Analysis: Tracking Variable Values Through Program Execution

(4.9.25) Exploring Graph Theory: Can a Graph Exist with Vertices of Only Two Different Degrees?

(4.9.25) Exploring Graph Theory: Can a Graph Exist with Vertices of Only Two Different Degrees?

(4.9.21) Unpacking Graph Theory: Can a Vertex's Degree Exceed the Total Number of Vertices?

(4.9.21) Unpacking Graph Theory: Can a Vertex's Degree Exceed the Total Number of Vertices?

(4.9.17) A Handshake Problem: Is It Possible for Each of 25 People to Shake Hands with Three Others?

(4.9.17) A Handshake Problem: Is It Possible for Each of 25 People to Shake Hands with Three Others?

(4.9.13) Constructing a Simple Graph with Nine Edges and Vertices of Degree 3: Unpacking the Process

(4.9.13) Constructing a Simple Graph with Nine Edges and Vertices of Degree 3: Unpacking the Process

(4.9.9) How to Approach a Graph Design Problem: Solving for a Simple Graph with Degrees 1, 2, 3, 4

(4.9.9) How to Approach a Graph Design Problem: Solving for a Simple Graph with Degrees 1, 2, 3, 4

(4.9.5) Graph Theory - Drawing Graphs with Specific Vertex Degrees

(4.9.5) Graph Theory - Drawing Graphs with Specific Vertex Degrees

(4.9.1) Graph Theory - Counting Degrees and Edges & Verifying The Handshake Lemma

(4.9.1) Graph Theory - Counting Degrees and Edges & Verifying The Handshake Lemma

(4.8.37) Proof for the Additive Identity of Real Numbers

(4.8.37) Proof for the Additive Identity of Real Numbers

(4.8.33) Proof for Distinct Prime Numbers in the form 4K + 3

(4.8.33) Proof for Distinct Prime Numbers in the form 4K + 3

(4.8.29) Consequences of Division by a Prime Number

(4.8.29) Consequences of Division by a Prime Number

(4.8.25) Proof That the Square Root of Non-Perfect Square Integer Is Irrational

(4.8.25) Proof That the Square Root of Non-Perfect Square Integer Is Irrational

(4.8.21) Proving Uniqueness in Quotient Remainder Theorem

(4.8.21) Proving Uniqueness in Quotient Remainder Theorem

(4.8.17) Evaluating Statements: Rational Numbers and Square Roots

(4.8.17) Evaluating Statements: Rational Numbers and Square Roots

(4.8.13) Proving that a Rational Number Divided by an Irrational Number is Sometimes Rational

(4.8.13) Proving that a Rational Number Divided by an Irrational Number is Sometimes Rational

(4.8.9) Evaluating Statements: Rational and Irrational Square Roots

(4.8.9) Evaluating Statements: Rational and Irrational Square Roots

(4.8.5) Cube Roots and Rational Numbers: Navigating Incorrect Proofs

(4.8.5) Cube Roots and Rational Numbers: Navigating Incorrect Proofs

(4.8.1) Rational vs Irrational Numbers: Unraveling The Mystery of the Square Root of 2

(4.8.1) Rational vs Irrational Numbers: Unraveling The Mystery of the Square Root of 2

(4.7.33) Unveiling the Sieve of Eratosthenes: Finding Prime Numbers Efficiently

(4.7.33) Unveiling the Sieve of Eratosthenes: Finding Prime Numbers Efficiently

(4.7.29) Diving into Proof by Contradiction with Even and Odd Integers

(4.7.29) Diving into Proof by Contradiction with Even and Odd Integers

(4.7.25) Mastering Mathematical Proofs: Contraposition vs. Contradiction

(4.7.25) Mastering Mathematical Proofs: Contraposition vs. Contradiction

(4.7.21) Navigating Through Contradiction and Contraposition in Proofs

(4.7.21) Navigating Through Contradiction and Contraposition in Proofs

(4.7.17) Unraveling a Proof by Contradiction for Prime Numbers

(4.7.17) Unraveling a Proof by Contradiction for Prime Numbers

(4.7.13) Diving into the Dynamics of Irrational and Nonzero Rational Numbers

(4.7.13) Diving into the Dynamics of Irrational and Nonzero Rational Numbers

(4.7.9) Unraveling Misconceptions: The Difference Between Irrational and Rational Numbers

(4.7.9) Unraveling Misconceptions: The Difference Between Irrational and Rational Numbers

(4.7.5) Mastering Negations and Contradictions: The Case of the Greatest Even Integer

(4.7.5) Mastering Negations and Contradictions: The Case of the Greatest Even Integer

(4.7.1) Illuminating Contradictions in Proofs: The Case of the Least Positive Real Number

(4.7.1) Illuminating Contradictions in Proofs: The Case of the Least Positive Real Number

(4.6.33) Unpacking the Connection Between Division and Floor Functions

(4.6.33) Unpacking the Connection Between Division and Floor Functions

(4.6.29) Proving a Mathematical Claim: Examining the Ceiling Function with Odd Integers

(4.6.29) Proving a Mathematical Claim: Examining the Ceiling Function with Odd Integers

(4.6.25) Unraveling Mathematical Claims: Investigating the Floor Function with Real Numbers

(4.6.25) Unraveling Mathematical Claims: Investigating the Floor Function with Real Numbers

(4.6.21) Probing Mathematical Statements: Truths, Fallacies, and Proofs Without Theorem 4.6.1

(4.6.21) Probing Mathematical Statements: Truths, Fallacies, and Proofs Without Theorem 4.6.1

(4.6.17) Unraveling the Mystery of Integer Division and Modulo Operations

(4.6.17) Unraveling the Mystery of Integer Division and Modulo Operations

(4.6.13) Probing the Floor Function: A Proof for Even Integers

(4.6.13) Probing the Floor Function: A Proof for Even Integers

(4.6.9) Decoding the Shipping Conundrum: Using Ceiling Notation to Determine the # of Boxes Needed

(4.6.9) Decoding the Shipping Conundrum: Using Ceiling Notation to Determine the # of Boxes Needed

(4.6.5) The Quotient Remainder Theorem: Expressing 259 div 11 and 259 mod 11 Using Floor Notation

(4.6.5) The Quotient Remainder Theorem: Expressing 259 div 11 and 259 mod 11 Using Floor Notation

(4.6.1) Understanding the Floor and Ceiling Functions: A Case Study of 37.999

(4.6.1) Understanding the Floor and Ceiling Functions: A Case Study of 37.999

(4.5.25) Unraveling the Intricacies of Modular Arithmetic: A Proof for A*B mod 7 = 2

(4.5.25) Unraveling the Intricacies of Modular Arithmetic: A Proof for A*B mod 7 = 2

(4.5.49) Proving Equivalence of Modulo Equations: A Quotient Remainder Theorem Approach

(4.5.49) Proving Equivalence of Modulo Equations: A Quotient Remainder Theorem Approach

(4.5.45) Matrix Storage Mystery: Formulating Row and Column Positions in Row Major Form

(4.5.45) Matrix Storage Mystery: Formulating Row and Column Positions in Row Major Form

(4.5.41) Diving into the Absolute Value Property: A Four-Case Proof for Real Numbers

(4.5.41) Diving into the Absolute Value Property: A Four-Case Proof for Real Numbers

(4.5.37) Probing the Indivisibility of n² + 5 by 4: A Comprehensive Proof

(4.5.37) Probing the Indivisibility of n² + 5 by 4: A Comprehensive Proof

(4.5.33) Unraveling the Oddity of Integer Parity: A Study of Odd and Even Numbers

(4.5.33) Unraveling the Oddity of Integer Parity: A Study of Odd and Even Numbers

(4.5.29) Diving into the Quotient Remainder Theorem: A Proof for n² mod 3 = 0 or 1

(4.5.29) Diving into the Quotient Remainder Theorem: A Proof for n² mod 3 = 0 or 1

(4.5.21) Exploring the Connection Between Modulus Operations: From B mod 12 = 5 to 8B mod 12

(4.5.21) Exploring the Connection Between Modulus Operations: From B mod 12 = 5 to 8B mod 12

(4.5.17) Unraveling the Odd Nature of n² - n + 3: A Two-Case Study for All Integers

(4.5.17) Unraveling the Odd Nature of n² - n + 3: A Two-Case Study for All Integers

(4.5.13) Using the Division Algorithm to Determine the Day of the Week in the Future

(4.5.13) Using the Division Algorithm to Determine the Day of the Week in the Future

(4.5.9) Dividing 28 by 5: Finding the Quotient through the Division Algorithm

(4.5.9) Dividing 28 by 5: Finding the Quotient through the Division Algorithm

(4.5.5) Understanding Quotients and Remainders: Non-Negative Remainders in the Division Algorithm

(4.5.5) Understanding Quotients and Remainders: Non-Negative Remainders in the Division Algorithm

(4.5.1) Unveiling the Division Algorithm: Finding Quotient and Remainder w/ a Calculator and by Hand

(4.5.1) Unveiling the Division Algorithm: Finding Quotient and Remainder w/ a Calculator and by Hand

(4.4.49) Unraveling the Connection Between the Alternating Sum of Digits and Divisibility by 11

(4.4.49) Unraveling the Connection Between the Alternating Sum of Digits and Divisibility by 11

(4.2.41) Examining Fermat Numbers and Their Primality

(4.2.41) Examining Fermat Numbers and Their Primality

(4.4.45) Proving Divisibility: If n Ends in Five, Then 5 Divides n

(4.4.45) Proving Divisibility: If n Ends in Five, Then 5 Divides n

(4.4.41) Calculating Zeros at the End of a Large Number: Using Prime Factorization

(4.4.41) Calculating Zeros at the End of a Large Number: Using Prime Factorization

(4.4.37) Applying the Unique Factorization Theorem to Factor Integers

(4.4.37) Applying the Unique Factorization Theorem to Factor Integers

(4.4.33) Exploring Coin Combinations: Can Nickels, Dimes, and Quarters Add Up to 472 Cents?

(4.4.33) Exploring Coin Combinations: Can Nickels, Dimes, and Quarters Add Up to 472 Cents?

(4.4.29) Proving Implications in Integer Division: If a Divides B, Does a² Divide B²?

(4.4.29) Proving Implications in Integer Division: If a Divides B, Does a² Divide B²?

(4.4.25) Evaluating a Statement about Factors: Does the Product of Two Factors Remain a Factor?

(4.4.25) Evaluating a Statement about Factors: Does the Product of Two Factors Remain a Factor?

(4.4.21) Verifying the Truth of a Statement: Multiplication of Even Integers and Multiples of Four

(4.4.21) Verifying the Truth of a Statement: Multiplication of Even Integers and Multiples of Four

(4.4.17) Proving a Division Property of Integers: If a Divides c and b Divides d, Then ab Divides cd

(4.4.17) Proving a Division Property of Integers: If a Divides c and b Divides d, Then ab Divides cd

(4.4.13) Divisibility Analysis: Does 8 Divide n²-1 When n=4k+3?

(4.4.13) Divisibility Analysis: Does 8 Divide n²-1 When n=4k+3?

(4.4.9) Understanding Factors: Is 4 a Factor of 2a*34b?

(4.4.9) Understanding Factors: Is 4 a Factor of 2a*34b?

(4.4.5) Determining Divisibility: Is 6m(2m+10) Divisible by 4?

(4.4.5) Determining Divisibility: Is 6m(2m+10) Divisible by 4?

(4.4.1) Understanding Divisibility: Is 52 Divisible by 13?

(4.4.1) Understanding Divisibility: Is 52 Divisible by 13?

(4.3.37) Spotting Errors in Proofs Involving Addition of Rational Numbers

(4.3.37) Spotting Errors in Proofs Involving Addition of Rational Numbers

(4.3.33) Deciphering Quadratic Polynomials using Even and Odd Integers

(4.3.33) Deciphering Quadratic Polynomials using Even and Odd Integers

(4.3.29) Unraveling the Rationality of 'x' through Equations

(4.3.29) Unraveling the Rationality of 'x' through Equations

(4.3.25) Exploring the Rationality of Mathematical Expressions

(4.3.25) Exploring the Rationality of Mathematical Expressions

(4.3.21) Exploring the Interplay of Even and Odd Integers

(4.3.21) Exploring the Interplay of Even and Odd Integers

(4.3.17) Unraveling the Mystery of Rational Number Differences

(4.3.17) Unraveling the Mystery of Rational Number Differences

(4.3.13) Exploring the Rationality of Negative Numbers

(4.3.13) Exploring the Rationality of Negative Numbers

(4.3.9) Unraveling the Rationality of (b - a) / (ab²)

(4.3.9) Unraveling the Rationality of (b - a) / (ab²)

(4.3.5) Journey into the World of Repeating Decimals and Integer Ratios

(4.3.5) Journey into the World of Repeating Decimals and Integer Ratios

(4.3.1) Delving into the Nature of Rational Numbers

(4.3.1) Delving into the Nature of Rational Numbers

(4.2.37) Unraveling the Mystery of Square Roots Multiplication

(4.2.37) Unraveling the Mystery of Square Roots Multiplication

(4.2.33) Demonstrating that 28 Can't Be Expressed as the Sum of Three or Fewer Perfect Squares

(4.2.33) Demonstrating that 28 Can't Be Expressed as the Sum of Three or Fewer Perfect Squares

(4.2.29) Disproving the Assertion: Negative One to the Power of a Prime Equals Negative One

(4.2.29) Disproving the Assertion: Negative One to the Power of a Prime Equals Negative One

(4.2.25) Exploring the Evenness of the Difference Between Two Even Integers

(4.2.25) Exploring the Evenness of the Difference Between Two Even Integers

(4.2.21) Unveiling the Odd Nature of Negatives of Odd Integers

(4.2.21) Unveiling the Odd Nature of Negatives of Odd Integers

(4.2.17) Unraveling the Fallacy in a Composite Integer Theorem Proof

(4.2.17) Unraveling the Fallacy in a Composite Integer Theorem Proof

(4.2.13) Unraveling the Truth of Existential Quantifiers in Prime Numbers

(4.2.13) Unraveling the Truth of Existential Quantifiers in Prime Numbers

(4.2.9) Unraveling the Mystery: Why the Predecessor of a Perfect Square Greater Than 4 Isn't Prime

(4.2.9) Unraveling the Mystery: Why the Predecessor of a Perfect Square Greater Than 4 Isn't Prime

(4.2.5) Step-by-Step Guide: Proving the Sum of Squares of Two Odd Integers is Even

(4.2.5) Step-by-Step Guide: Proving the Sum of Squares of Two Odd Integers is Even

(4.2.1) Proving Universal Statements: If n is Odd, Then 3n + 5 is Even

(4.2.1) Proving Universal Statements: If n is Odd, Then 3n + 5 is Even

(4.1.29) Proving Theorems: The Negation of Even Integers Remains Even

(4.1.29) Proving Theorems: The Negation of Even Integers Remains Even

(4.1.25) Unpacking the Process of Proving Integer Equations: Quantification and Proof Structure

(4.1.25) Unpacking the Process of Proving Integer Equations: Quantification and Proof Structure

(4.1.21) Exhaustion Method: Expressing Even Integers Under 26 as Perfect Squares Sum

(4.1.21) Exhaustion Method: Expressing Even Integers Under 26 as Perfect Squares Sum

(4.1.17) Exploring the Validity of a Mathematical Property: (a+b)² = a² + b²

(4.1.17) Exploring the Validity of a Mathematical Property: (a+b)² = a² + b²

(4.1.13) Unraveling Negations and Counterexamples in Mathematical Statements

(4.1.13) Unraveling Negations and Counterexamples in Mathematical Statements

(4.1.9) Unraveling Exponential Inequalities: A Real Number Solution

(4.1.9) Unraveling Exponential Inequalities: A Real Number Solution

(4.1.5) Discovering Integer Pairs: Proving 1/m + 1/n is an Integer

(4.1.5) Discovering Integer Pairs: Proving 1/m + 1/n is an Integer

(4.1.1) Diving into the Distinction between Odd and Even Numbers

(4.1.1) Diving into the Distinction between Odd and Even Numbers

(3.4.33) Unraveling the Mystery of Aviary Birds: A Logical Chain of Implications

(3.4.33) Unraveling the Mystery of Aviary Birds: A Logical Chain of Implications

(3.4.29) Mastering the Art of Argument Reordering: A Deep Dive into Tarski Worlds

(3.4.29) Mastering the Art of Argument Reordering: A Deep Dive into Tarski Worlds

(3.4.25) Unraveling Argument Validity: A Visual Approach to College Cafeteria Food

(3.4.25) Unraveling Argument Validity: A Visual Approach to College Cafeteria Food

(3.4.21) Unraveling Argument Validity: A Visual Approach to Categorical Syllogisms

(3.4.21) Unraveling Argument Validity: A Visual Approach to Categorical Syllogisms

(3.4.17) Diving into Converse and Inverse Errors: A Study of Infinite Series Arguments

(3.4.17) Diving into Converse and Inverse Errors: A Study of Infinite Series Arguments

(3.4.13) Distinguishing Valid and Invalid Arguments: A Deep Dive into Universal Modus Ponens

(3.4.13) Distinguishing Valid and Invalid Arguments: A Deep Dive into Universal Modus Ponens

(3.4.9) Unraveling Argument Validity: A Deep Dive into Universal Modus Ponens and Tollens

(3.4.9) Unraveling Argument Validity: A Deep Dive into Universal Modus Ponens and Tollens

(3.4.5) Unveiling the Power of Universal Modus Tollens: Crafting Valid Conclusions

(3.4.5) Unveiling the Power of Universal Modus Tollens: Crafting Valid Conclusions

(3.4.1) Journey Through Universal Instantiation and Modus Ponens in Mathematical Contexts

(3.4.1) Journey Through Universal Instantiation and Modus Ponens in Mathematical Contexts

(3.3.61) Understanding Logical Statements and Inferences in Prologue

(3.3.61) Understanding Logical Statements and Inferences in Prologue

(3.3.57) Examining Statement Forms and the Distributive Property of Universal Quantifiers

(3.3.57) Examining Statement Forms and the Distributive Property of Universal Quantifiers

(3.3.53) Quantification and Negation in Ski World: True or False Statements Explained

(3.3.53) Quantification and Negation in Ski World: True or False Statements Explained

(3.3.49) Exploring Tarski World with Formal Logical Notation

(3.3.49) Exploring Tarski World with Formal Logical Notation

(3.3.45) Decoding 'There Exists a Unique' Predicate Statement

(3.3.45) Decoding 'There Exists a Unique' Predicate Statement

(3.3.41) Unraveling Truth Values of Propositional Statements

(3.3.41) Unraveling Truth Values of Propositional Statements

(3.3.37) Formalizing and Negating Statements with Quantifiers and Variables

(3.3.37) Formalizing and Negating Statements with Quantifiers and Variables

(3.3.33) Evaluating Truth Values of Statements with Quantifiers and Variables

(3.3.33) Evaluating Truth Values of Statements with Quantifiers and Variables

(3.3.29) For All and There Exists Statement Interchange: Evaluating Truth Values

(3.3.29) For All and There Exists Statement Interchange: Evaluating Truth Values

(3.3.25) Understanding East Haven: True and False Statements with Quantifiers

(3.3.25) Understanding East Haven: True and False Statements with Quantifiers

(3.3.21) Exploring the Intricacies of Tarski's World: A Look at Quantifiers and Negation

(3.3.21) Exploring the Intricacies of Tarski's World: A Look at Quantifiers and Negation

(3.3.17) Dissecting the Logic of Tarski's World: A Deep Dive into Quantifiers

(3.3.17) Dissecting the Logic of Tarski's World: A Deep Dive into Quantifiers

(3.3.9) Probing the Complexity of Program Correctness

(3.3.9) Probing the Complexity of Program Correctness

(3.3.13) Deciphering and Negating Complex Statements in English

(3.3.13) Deciphering and Negating Complex Statements in English

(3.3.5) Decoding Statement Verification in Tarski's World

(3.3.5) Decoding Statement Verification in Tarski's World

(3.3.1) Unraveling Truth Values of Statements About Capital Cities

(3.3.1) Unraveling Truth Values of Statements About Capital Cities

(3.2.49) The Complexity of Reasonable Program Correctness

(3.2.49) The Complexity of Reasonable Program Correctness

(3.2.45) Rewriting Statements in Discrete Mathematics: A Practical Guide

(3.2.45) Rewriting Statements in Discrete Mathematics: A Practical Guide

(3.2.41) Unpacking the Logic of If-Then Form with Necessary Condition

(3.2.41) Unpacking the Logic of If-Then Form with Necessary Condition

(3.2.37) Decoding the Logic of Sequence Analysis

(3.2.37) Decoding the Logic of Sequence Analysis

(3.2.33) Unveiling the Secrets of Function Continuity and Differentiability

(3.2.33) Unveiling the Secrets of Function Continuity and Differentiability

(3.2.29) Journey into the World of Function Continuity and Differentiability

(3.2.29) Journey into the World of Function Continuity and Differentiability

(3.2.25) Exploring the Intricacies of Function Continuity and Differentiability

(3.2.25) Exploring the Intricacies of Function Continuity and Differentiability

(3.2.21) Diving into the Depths of Function Continuity and Differentiability

(3.2.21) Diving into the Depths of Function Continuity and Differentiability

(3.2.17) Unraveling the Mystery of Function Continuity and Differentiability

(3.2.17) Unraveling the Mystery of Function Continuity and Differentiability

(3.2.13) Mastering Negations: A Detailed Guide to Correctly Negating Implication Statements

(3.2.13) Mastering Negations: A Detailed Guide to Correctly Negating Implication Statements

(3.2.9) Deciphering Negations: A Guide to Universally Quantified Statements and Implications

(3.2.9) Deciphering Negations: A Guide to Universally Quantified Statements and Implications

(3.2.5) The Art of Negation: A Deep Dive into Real Numbers and Universally Quantified Statements

(3.2.5) The Art of Negation: A Deep Dive into Real Numbers and Universally Quantified Statements

(3.2.1) Decoding Negations: A Comprehensive Guide to Universal Claims in Discrete Mathematics

(3.2.1) Decoding Negations: A Comprehensive Guide to Universal Claims in Discrete Mathematics

(3.1.33) Unraveling Truth and Falsehood: A Deep Dive into Real Numbers and Predicate Variables

(3.1.33) Unraveling Truth and Falsehood: A Deep Dive into Real Numbers and Predicate Variables

(3.1.29) Decoding Geometric Figures: A Guide to Rewriting Statements about Squares and Rectangles

(3.1.29) Decoding Geometric Figures: A Guide to Rewriting Statements about Squares and Rectangles

(3.1.25) Mastering Formal Statements: A Comprehensive Guide to Universal Quantification

(3.1.25) Mastering Formal Statements: A Comprehensive Guide to Universal Quantification

(3.1.21) Sentence Rearrangement: Shifting Quantifiers to the End in Mathematical Statements

(3.1.21) Sentence Rearrangement: Shifting Quantifiers to the End in Mathematical Statements

(3.1.17) Decoding Existential Statements: A Guide to Rewriting in Formal Notation

(3.1.17) Decoding Existential Statements: A Guide to Rewriting in Formal Notation