The Largest Numbers Ever Discovered // The Bizarre World of Googology

Dr. Trefor Bazett
Dr. Trefor Bazett
270.8 هزار بار بازدید - 3 سال پیش - Check out Brilliant ► https://brilliant.org/TreforBazett/
Check out Brilliant ► https://brilliant.org/TreforBazett/ Learn math more effectively for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video on unfathomably large numbers. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor What is the biggest number in the universe? What is the biggest number that any human has ever conceived of, or used in a proof, or been able to write down? In this video we are going to explore the fascinating world of googology, the study of unbelievably big numbers. We will begin near the bottom with "tiny" number like a googol (10^100) and a googolplex (10^googol) before realizing we will really need to do introduce better notation. We will then see Knuth's up-arrow notation that let's us form power towers of numbers, repeated exponentiation called tetration that is much like how exponentiation is repeated multiplication and multiplication repeated addition. And it goes up and up from there! We will see Graham's number which infamously got the googology ball rolling when it was used as an upper bound for a problem in graph theory and finally we will the unimaginable Tree(3) which comes out of a simple to state problem in graph theory and amazingly results in this incredible number. You can check our Ron Graham himself introduce how Graham's number comes about over on Numerphile here: https://www.seevid.ir/fa/w/HX8bihEe3nA. You might also like to check out the googology wiki here: https://googology.wikia.org/wiki/Googology_Wiki https://www.seevid.ir/fa/w/yIdigLW07xY Intro to Googology https://www.seevid.ir/fa/w/yIdigLW07xY Googol and Googolplex https://www.seevid.ir/fa/w/yIdigLW07xY Towers of Exponents https://www.seevid.ir/fa/w/yIdigLW07xY Knuth's up-arrow notation https://www.seevid.ir/fa/w/yIdigLW07xY Graham's Number https://www.seevid.ir/fa/w/yIdigLW07xY Tree(3) https://www.seevid.ir/fa/w/yIdigLW07xY Brilliant.org/treforbazett COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series https://www.seevid.ir/fa/w/LPH2lqis3D0 ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join: MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
3 سال پیش در تاریخ 1400/07/29 منتشر شده است.
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