What happens when you go beyond exponentiation? This video explores some of the weirdest and most intriguing hyperoperations mathematicians have invented. 00:00 Basic operations 02:46 Exponentiation 04:16 Tetration 06:33 Pentation 07:39 Infinite hyperoperations 09:06 Zeration 10:35 Fractional hyperoperations 12:58 Lower hyperoperations 14:33 Mixed hyperoperations 15:27 Balanced hyperoperations 16:31 Commutative hyperoperations 21:36 Generalized hyperoperations 24:33 Parallel hyperoperations Symbols: + - × ÷ ↑ √ ∞ ω ↓ ★ ☆ ◆ ◇ ⊙ ∥ ╫ ⧔ ⧖ #SoME4 Sources and further research: Addition: https:// :Addition#Natural_Numbers Subtraction: https:// :Subtraction#Natural_Numbers Multiplication: https:// :Multiplication#Natural_Numbers Division: https:// :Division/Field/Real_Numbers Exponentiation: https:// :Power_(Algebra) Tetration (and some cool pictures): https:// :Tetration https:// https:// :Cheetahrock63/Hypercomplex_Blog:_Tetration_Portal Solution of F(z+1)=exp(F(z)) in complex z-plane, DMITRII KOUZNETSOV 2009 Tetration calculators: https:// https:// Hyperoperations: https:// Circulation: https:// Ordinal hyperoperations: https:// Zeration (and pre-addition): https:// https:// https:// Fractional hyperoperations: https:// Fractional Mathematical Operators and Their Computational Approximation, José Crespo and Francisco Javier Montáns 2016 Lower hyperoperations: https:// Mixed hyperoperations: https:// Balanced hyperoperations: https:// Catalan parenthesis hyperoperations or something: https:// Commutative hyperoperations: https:// Generalized hyperoperations: https:// Parallel addition: https:// (operator) https:// Exponentiation, nth root and logarithm notation (and parallel addition): Hyperoperations: Rational tetration: Zeration: Commutative hyperoperations: Infinite base pre-addition: Generalized hyperoperations: Congratulations, you just read the description! Here are two bonus hyperoperation sequences for you (I had nothing to talk about and don't understand them very well but here they are): Robbins hyperoperations: https:// #:~:text=Frappier%20hyper%2Doperator.-,Robbins%20Hyper%2Doperators,-Robbins%20hyper%2Doperators Pisa hyperoperations: Constructing a hyperoperation sequence-pisa, A P Andonov 2021 IOP Conf. Ser.: Mater. Sci. Eng. 1031 012071 Now like and subscribe 👊😎 Thank you!