Every Hyperoperation Explained
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:// proofwiki.org/wiki/Definition:Addition#Natural_Numbers
Subtraction: https:// proofwiki.org/wiki/Definition:Subtraction#Natural_Numbers
Multiplication: https:// proofwiki.org/wiki/Definition:Multiplication#Natural_Numbers
Division: https:// proofwiki.org/wiki/Definition:Division/Field/Real_Numbers
Exponentiation: https:// proofwiki.org/wiki/Definition:Power_(Algebra)
Tetration (and some cool pictures): https:// proofwiki.org/wiki/Definition:Tetration
https:// tetration.org/index.php/Main_Page
https:// verse-and-dimensions.fandom.com/wiki/User_blog:Cheetahrock63/Hypercomplex_Blog:_Tetration_Portal
Solution of F(z+1)=exp(F(z)) in complex z-plane, DMITRII KOUZNETSOV 2009
Tetration calculators: https:// myweb.astate.edu/wpaulsen/tetcalc/tetcalc.html
https:// tetrationforum.org/showthread.php?tid=486&pid=6154#:~:text=%C2%A0%C2%A0kneser.gp%20(Size%3A%2035.84%20KB%20/%20Downloads%3A%201%2C218)
Hyperoperations: https:// en.wikipedia.org/wiki/Hyperoperation
Circulation: https:// googology.fandom.com/wiki/Circulation
Ordinal hyperoperations: https:// sites.google.com/site/travelingtotheinfinity/nomenclature-for-the-hyper-operators
Zeration (and pre-addition): https:// tetrationforum.org/showthread.php?tid=122
https:// tetrationforum.org/showthread.php?tid=926
https:// tetrationforum.org/showthread.php?tid=1008
Fractional hyperoperations: https:// www.physicsforums.com/threads/generalization-of-hyperoperations-fractional-operations.485870/
Fractional Mathematical Operators and Their Computational Approximation, José Crespo and Francisco Javier Montáns 2016
Lower hyperoperations: https:// sites.google.com/site/pointlesslargenumberstuff/home/2/weakoperators
Mixed hyperoperations: https:// tetrationforum.org/showthread.php?tid=114#:~:text=07%3A04%20PM-,Ivars%20Wrote%3A,-Another%20question%20is
Balanced hyperoperations: https:// tetrationforum.org/showthread.php?tid=145&pid=1886
Catalan parenthesis hyperoperations or something: https:// tetrationforum.org/attachment.php?aid=970
Commutative hyperoperations: https:// math.stackexchange.com/questions/1114543/commutative-version-of-hyperoperators
Generalized hyperoperations: https:// math.stackexchange.com/questions/1269643/continuum-between-addition-multiplication-and-exponentiation
Parallel addition: https:// en.wikipedia.org/wiki/Parallel_(operator)
https:// www.desmos.com/calculator/c483p33pgw
Exponentiation, nth root and logarithm notation (and parallel addition): • Triangle of Power
Hyperoperations: • The Rare Levels Beyond Exponents
Rational tetration: • Beyond Exponentiation: A Tetration Investi...
Zeration: • The Hyperoperations Part 2: Operation Zero
Commutative hyperoperations: • The Missing Operation | Epic Math Time
• Addition, multiplication, ... what comes n...
Infinite base pre-addition: • Calculations in Another World
Generalized hyperoperations: • Обобщение Арифметики
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:// andydude.github.io/tetration/archives/tetration3/hyper.html#:~: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
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