What is the name for this: “x^^y” (as in 2^^2=2^2 and 3^^3=3^3^3 and so on)












0












$begingroup$


How do you call / is there any specific name for the following:



x^^y



e.g.:




  • 2^^2 = 2^2

  • 3^^3 = 3^3^3

  • 4^^4 = 4^4^4^4

  • ...






notation terminology tetration hyperoperation







share|cite|improve this question











$endgroup$












  • $begingroup$
    superpowers, Knuth notation.
    $endgroup$
    – Wuestenfux
    Dec 31 '18 at 17:31






  • 2




    $begingroup$
    Look up "tetration:. en.wikipedia.org/wiki/Tetration
    $endgroup$
    – Ethan Bolker
    Dec 31 '18 at 17:32










  • $begingroup$
    Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times.
    $endgroup$
    – Antinous
    Dec 31 '18 at 17:33


















0












$begingroup$


How do you call / is there any specific name for the following:



x^^y



e.g.:




  • 2^^2 = 2^2

  • 3^^3 = 3^3^3

  • 4^^4 = 4^4^4^4

  • ...






notation terminology tetration hyperoperation







share|cite|improve this question











$endgroup$












  • $begingroup$
    superpowers, Knuth notation.
    $endgroup$
    – Wuestenfux
    Dec 31 '18 at 17:31






  • 2




    $begingroup$
    Look up "tetration:. en.wikipedia.org/wiki/Tetration
    $endgroup$
    – Ethan Bolker
    Dec 31 '18 at 17:32










  • $begingroup$
    Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times.
    $endgroup$
    – Antinous
    Dec 31 '18 at 17:33
















0












0








0





$begingroup$


How do you call / is there any specific name for the following:



x^^y



e.g.:




  • 2^^2 = 2^2

  • 3^^3 = 3^3^3

  • 4^^4 = 4^4^4^4

  • ...






notation terminology tetration hyperoperation







share|cite|improve this question











$endgroup$




How do you call / is there any specific name for the following:



x^^y



e.g.:




  • 2^^2 = 2^2

  • 3^^3 = 3^3^3

  • 4^^4 = 4^4^4^4

  • ...






notation terminology tetration hyperoperation




notation terminology tetration hyperoperation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 13 at 23:26









Simply Beautiful Art

50.6k579183




50.6k579183










asked Dec 31 '18 at 17:29









EASYEASY

32




32












  • $begingroup$
    superpowers, Knuth notation.
    $endgroup$
    – Wuestenfux
    Dec 31 '18 at 17:31






  • 2




    $begingroup$
    Look up "tetration:. en.wikipedia.org/wiki/Tetration
    $endgroup$
    – Ethan Bolker
    Dec 31 '18 at 17:32










  • $begingroup$
    Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times.
    $endgroup$
    – Antinous
    Dec 31 '18 at 17:33




















  • $begingroup$
    superpowers, Knuth notation.
    $endgroup$
    – Wuestenfux
    Dec 31 '18 at 17:31






  • 2




    $begingroup$
    Look up "tetration:. en.wikipedia.org/wiki/Tetration
    $endgroup$
    – Ethan Bolker
    Dec 31 '18 at 17:32










  • $begingroup$
    Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times.
    $endgroup$
    – Antinous
    Dec 31 '18 at 17:33


















$begingroup$
superpowers, Knuth notation.
$endgroup$
– Wuestenfux
Dec 31 '18 at 17:31




$begingroup$
superpowers, Knuth notation.
$endgroup$
– Wuestenfux
Dec 31 '18 at 17:31




2




2




$begingroup$
Look up "tetration:. en.wikipedia.org/wiki/Tetration
$endgroup$
– Ethan Bolker
Dec 31 '18 at 17:32




$begingroup$
Look up "tetration:. en.wikipedia.org/wiki/Tetration
$endgroup$
– Ethan Bolker
Dec 31 '18 at 17:32












$begingroup$
Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times.
$endgroup$
– Antinous
Dec 31 '18 at 17:33






$begingroup$
Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times.
$endgroup$
– Antinous
Dec 31 '18 at 17:33












1 Answer
1






active

oldest

votes


















3












$begingroup$

This is known as tetration, where $^na$ is $a^{a^{a^{...}}}$ with $n$ copies of $a$ in the exponentiation. You might also seen it written as $a uparrow uparrow n$.



To learn more about these kinds of compound arithmetic operators, I recommend reading about Knuth's up-arrow notation.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Now that is one rapidly growing function!
    $endgroup$
    – Mike
    Jan 1 at 3:35






  • 1




    $begingroup$
    @Mike :P More like some of the slowest of fast growing functions
    $endgroup$
    – Simply Beautiful Art
    Feb 10 at 23:47











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

This is known as tetration, where $^na$ is $a^{a^{a^{...}}}$ with $n$ copies of $a$ in the exponentiation. You might also seen it written as $a uparrow uparrow n$.



To learn more about these kinds of compound arithmetic operators, I recommend reading about Knuth's up-arrow notation.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Now that is one rapidly growing function!
    $endgroup$
    – Mike
    Jan 1 at 3:35






  • 1




    $begingroup$
    @Mike :P More like some of the slowest of fast growing functions
    $endgroup$
    – Simply Beautiful Art
    Feb 10 at 23:47
















3












$begingroup$

This is known as tetration, where $^na$ is $a^{a^{a^{...}}}$ with $n$ copies of $a$ in the exponentiation. You might also seen it written as $a uparrow uparrow n$.



To learn more about these kinds of compound arithmetic operators, I recommend reading about Knuth's up-arrow notation.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Now that is one rapidly growing function!
    $endgroup$
    – Mike
    Jan 1 at 3:35






  • 1




    $begingroup$
    @Mike :P More like some of the slowest of fast growing functions
    $endgroup$
    – Simply Beautiful Art
    Feb 10 at 23:47














3












3








3





$begingroup$

This is known as tetration, where $^na$ is $a^{a^{a^{...}}}$ with $n$ copies of $a$ in the exponentiation. You might also seen it written as $a uparrow uparrow n$.



To learn more about these kinds of compound arithmetic operators, I recommend reading about Knuth's up-arrow notation.






share|cite|improve this answer









$endgroup$



This is known as tetration, where $^na$ is $a^{a^{a^{...}}}$ with $n$ copies of $a$ in the exponentiation. You might also seen it written as $a uparrow uparrow n$.



To learn more about these kinds of compound arithmetic operators, I recommend reading about Knuth's up-arrow notation.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 31 '18 at 17:33









Noble MushtakNoble Mushtak

15.3k1835




15.3k1835












  • $begingroup$
    Now that is one rapidly growing function!
    $endgroup$
    – Mike
    Jan 1 at 3:35






  • 1




    $begingroup$
    @Mike :P More like some of the slowest of fast growing functions
    $endgroup$
    – Simply Beautiful Art
    Feb 10 at 23:47


















  • $begingroup$
    Now that is one rapidly growing function!
    $endgroup$
    – Mike
    Jan 1 at 3:35






  • 1




    $begingroup$
    @Mike :P More like some of the slowest of fast growing functions
    $endgroup$
    – Simply Beautiful Art
    Feb 10 at 23:47
















$begingroup$
Now that is one rapidly growing function!
$endgroup$
– Mike
Jan 1 at 3:35




$begingroup$
Now that is one rapidly growing function!
$endgroup$
– Mike
Jan 1 at 3:35




1




1




$begingroup$
@Mike :P More like some of the slowest of fast growing functions
$endgroup$
– Simply Beautiful Art
Feb 10 at 23:47




$begingroup$
@Mike :P More like some of the slowest of fast growing functions
$endgroup$
– Simply Beautiful Art
Feb 10 at 23:47


















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