Category: Number Theory
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We Know Everything About This Number Except Whether It Exists
Some numbers are defined so precisely that we know almost everything about them, except whether a single example exists. This article explores quasiperfect numbers, almost perfect numbers, Descartes numbers, and superperfect numbers, all built from one simple idea: adding up the divisors of a number. Perfect, Abundant, and the Sum of Divisors The divisors of… read more
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Every Weird Number That Shouldn't Exist Explained
Thanks for watching! Chapters: 0:00 Zero 1:40 Negative Numbers 2:40 Imaginary Numbers 3:39 Infinitesimals 4:44 Surreal Numbers 5:55 Quaternions 7:00 Octonions 8:32 Transfinite Ordinals 9:28 Irrational Numbers One useful way to organize the major number systems is as a ladder with seven levels: Natural numbers, N Integers, Z Rational numbers, Q Real numbers, R Complex… read more
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Math Has Exactly 7 Levels of Numbers
Thanks for watching! Levels: 0:00 Intro 0:24 Level 1: Natural Numbers 1:14 Level 2: Integers 2:21 Level 3: Rationals 3:38 Level 4: Real Numbers 5:07 Level 5: Complex Numbers 7:16 Level 6: Quaternions 8:41 Level 7: Octonions 9:17 Why There Is No Level 8 One useful way to organize the major number systems is as… read more
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Every Unsolved Prime Number Problem
Brocard’s Conjecture Twin, Cousin, and Sexy Primes Palindromic Primes Euclid Numbers Goldbach’s Conjecture Brocard’s Conjecture A prime number is a positive whole number that has exactly two divisors: 1 and itself. Pick a prime number greater than 2, like 3. Then take the next prime number after that, in this case 5. Then take the… read more
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Every Number Set Explained
Natural Numbers Integers Rational Numbers Real Numbers Complex Numbers Natural Numbers The story starts at the beginning of mathematics itself. Evidence of humans counting things goes back to the Paleolithic era, tens of thousands of years ago, with tally marks etched on various surfaces. Early humans could have been counting fruits, animals, or days. Whatever… read more
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Fibonacci and the Birth of Modern Math
Leonardo de Pisa Fundamentally Changed Math Discovering the Fibonacci Series Ancient Indian Discoveries in Sanskrit Texts The Golden Number (Phi, φ) The Golden Spiral From Roman Numerals to Hindu-Arabic Numbers Fascinating Facts About the Fibonacci Sequence Leonardo de Pisa Fundamentally Changed Math mathematics is related to Natural Sciences the result of human logic a language… read more
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Every Real Function Explained
Every Type of Mathematical Function Explained Linear Functions Quadratic Functions Polynomials of Degree n Rational Functions Radical Functions Exponential Functions Logarithmic Functions Trigonometric Functions Inverse Trigonometric Functions Hyperbolic Functions The Absolute Value Function Constant Functions Floor and Ceiling Functions The Sign Function Piecewise Functions Linear Functions Linear functions have the form f(x) = mx +… read more
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Every Proof that √2 is Irrational but they get increasingly more complex
Four Proofs That √2 Is Irrational Proof by Contradiction Prime Factorization Proof Infinite Descent Proof Reciprocal Proof Four Proofs That √2 Is Irrational The square root of 2, or 2^(1/2), is irrational. That is, it’s a real number that cannot be expressed as the ratio of two integers. Its decimal expansion is non-terminating and non-repeating.… read more
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Every Unsolved Math Problem that Sounds Easy – Part 2
Six Deceptively Simple Unsolved Problems in Mathematics Mersenne Primes Perfect Numbers The Rational Distance Problem The Moving Sofa Problem The Inscribed Square Problem The Ramsey Theory Problem Six Deceptively Simple Unsolved Problems in Mathematics Mersenne Primes One unsolved problem in mathematics concerns whether or not there are infinitely many Mersenne primes. In order to understand… read more
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Every Proof That There Are Infinitely Many Primes Explained
What Is a Prime Number? Euclid’s Proof Factorial Proof Erdős’s Proof What Is a Prime Number? Think of a natural number. That is, a number used for counting, like six. Next, think of another natural number, like two. If we calculate 6 / 2, the result is 3. Since 3 is also a natural number,… read more
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