Exponent is to exponentiation as _______ is to tetration
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Would it be tetrand, tetrant, or something else?
notation terminology tetration
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
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show 4 more comments
$begingroup$
Would it be tetrand, tetrant, or something else?
notation terminology tetration
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
$endgroup$
1
$begingroup$
Not sure people care too much about this. Why do you need this? Perhaps just adopt a word and go with it.
$endgroup$
– Pedro Tamaroff♦
Dec 13 '18 at 14:51
1
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See Tetration : "The parameter $a$ may be called the base-parameter, while the parameter $n$ may be called the height-parameter."
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– Mauro ALLEGRANZA
Dec 13 '18 at 14:53
1
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@PedroTamaroff I don't need it, I find nomenclature itself interesting.
$endgroup$
– Griffin
Dec 13 '18 at 14:57
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@MauroALLEGRANZA You are clearly a better reader than I. Happy to accept as an answer if you make it one.
$endgroup$
– Griffin
Dec 13 '18 at 14:58
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FYI, I've called it the tetrated exponent in some early 2000s sci.math posts.
$endgroup$
– Dave L. Renfro
Dec 13 '18 at 14:59
|
show 4 more comments
$begingroup$
Would it be tetrand, tetrant, or something else?
notation terminology tetration
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
$endgroup$
Would it be tetrand, tetrant, or something else?
notation terminology tetration
notation terminology tetration
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
asked Dec 13 '18 at 14:45
GriffinGriffin
1598
1598
1
$begingroup$
Not sure people care too much about this. Why do you need this? Perhaps just adopt a word and go with it.
$endgroup$
– Pedro Tamaroff♦
Dec 13 '18 at 14:51
1
$begingroup$
See Tetration : "The parameter $a$ may be called the base-parameter, while the parameter $n$ may be called the height-parameter."
$endgroup$
– Mauro ALLEGRANZA
Dec 13 '18 at 14:53
1
$begingroup$
@PedroTamaroff I don't need it, I find nomenclature itself interesting.
$endgroup$
– Griffin
Dec 13 '18 at 14:57
$begingroup$
@MauroALLEGRANZA You are clearly a better reader than I. Happy to accept as an answer if you make it one.
$endgroup$
– Griffin
Dec 13 '18 at 14:58
$begingroup$
FYI, I've called it the tetrated exponent in some early 2000s sci.math posts.
$endgroup$
– Dave L. Renfro
Dec 13 '18 at 14:59
|
show 4 more comments
1
$begingroup$
Not sure people care too much about this. Why do you need this? Perhaps just adopt a word and go with it.
$endgroup$
– Pedro Tamaroff♦
Dec 13 '18 at 14:51
1
$begingroup$
See Tetration : "The parameter $a$ may be called the base-parameter, while the parameter $n$ may be called the height-parameter."
$endgroup$
– Mauro ALLEGRANZA
Dec 13 '18 at 14:53
1
$begingroup$
@PedroTamaroff I don't need it, I find nomenclature itself interesting.
$endgroup$
– Griffin
Dec 13 '18 at 14:57
$begingroup$
@MauroALLEGRANZA You are clearly a better reader than I. Happy to accept as an answer if you make it one.
$endgroup$
– Griffin
Dec 13 '18 at 14:58
$begingroup$
FYI, I've called it the tetrated exponent in some early 2000s sci.math posts.
$endgroup$
– Dave L. Renfro
Dec 13 '18 at 14:59
1
1
$begingroup$
Not sure people care too much about this. Why do you need this? Perhaps just adopt a word and go with it.
$endgroup$
– Pedro Tamaroff♦
Dec 13 '18 at 14:51
$begingroup$
Not sure people care too much about this. Why do you need this? Perhaps just adopt a word and go with it.
$endgroup$
– Pedro Tamaroff♦
Dec 13 '18 at 14:51
1
1
$begingroup$
See Tetration : "The parameter $a$ may be called the base-parameter, while the parameter $n$ may be called the height-parameter."
$endgroup$
– Mauro ALLEGRANZA
Dec 13 '18 at 14:53
$begingroup$
See Tetration : "The parameter $a$ may be called the base-parameter, while the parameter $n$ may be called the height-parameter."
$endgroup$
– Mauro ALLEGRANZA
Dec 13 '18 at 14:53
1
1
$begingroup$
@PedroTamaroff I don't need it, I find nomenclature itself interesting.
$endgroup$
– Griffin
Dec 13 '18 at 14:57
$begingroup$
@PedroTamaroff I don't need it, I find nomenclature itself interesting.
$endgroup$
– Griffin
Dec 13 '18 at 14:57
$begingroup$
@MauroALLEGRANZA You are clearly a better reader than I. Happy to accept as an answer if you make it one.
$endgroup$
– Griffin
Dec 13 '18 at 14:58
$begingroup$
@MauroALLEGRANZA You are clearly a better reader than I. Happy to accept as an answer if you make it one.
$endgroup$
– Griffin
Dec 13 '18 at 14:58
$begingroup$
FYI, I've called it the tetrated exponent in some early 2000s sci.math posts.
$endgroup$
– Dave L. Renfro
Dec 13 '18 at 14:59
$begingroup$
FYI, I've called it the tetrated exponent in some early 2000s sci.math posts.
$endgroup$
– Dave L. Renfro
Dec 13 '18 at 14:59
|
show 4 more comments
1 Answer
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When I first (ca 2007) came in contact with (what I later called) "exponentialtower" and which is even in its un-generalized form commonly called "tetration", this occured under the name "powertower" (for instance see mathworld). It seemed very natural for me to use the term (iteration-) "height" for the extend of iteration of that imagination of increasing a "powertower". After that, to use the letter "h" as its default shortcut/variable is again natural. For instance in the "tetration-forum" (founded at 2007) the term "height" has become a much common use.
(By this I consequently don't like/use the term "super-log()" or "slog()" for the function which tells us the required height of iteration from one $z_0$ to $z_h$ but use simply $text{hgh}()$ as that function in article and software)
disclaimer: this is only amateur-mathematics, no journal-publication or academic practice behind this
Additional remark: in a comment, if I recall correctly, there was a discussion whether exponentiation should be seen as "iterated multiplication" at all (as well as in its generalized to fractional iteration-"heights") but as a genuine operation (I think it was MSE/MO-user Qiaochu Yuan) and similarly for tetration, if at all, should also a more genuine operation be formulated - apart from the basic idea of iteration of an exponentiation. I like this idea much, but such a genuine operation has not been formulated yet. If it is formulated then the term height might be replaced by some more appropriate name - but I don't see any ansatz for this so far...
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
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When I first (ca 2007) came in contact with (what I later called) "exponentialtower" and which is even in its un-generalized form commonly called "tetration", this occured under the name "powertower" (for instance see mathworld). It seemed very natural for me to use the term (iteration-) "height" for the extend of iteration of that imagination of increasing a "powertower". After that, to use the letter "h" as its default shortcut/variable is again natural. For instance in the "tetration-forum" (founded at 2007) the term "height" has become a much common use.
(By this I consequently don't like/use the term "super-log()" or "slog()" for the function which tells us the required height of iteration from one $z_0$ to $z_h$ but use simply $text{hgh}()$ as that function in article and software)
disclaimer: this is only amateur-mathematics, no journal-publication or academic practice behind this
Additional remark: in a comment, if I recall correctly, there was a discussion whether exponentiation should be seen as "iterated multiplication" at all (as well as in its generalized to fractional iteration-"heights") but as a genuine operation (I think it was MSE/MO-user Qiaochu Yuan) and similarly for tetration, if at all, should also a more genuine operation be formulated - apart from the basic idea of iteration of an exponentiation. I like this idea much, but such a genuine operation has not been formulated yet. If it is formulated then the term height might be replaced by some more appropriate name - but I don't see any ansatz for this so far...
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
$endgroup$
add a comment |
$begingroup$
When I first (ca 2007) came in contact with (what I later called) "exponentialtower" and which is even in its un-generalized form commonly called "tetration", this occured under the name "powertower" (for instance see mathworld). It seemed very natural for me to use the term (iteration-) "height" for the extend of iteration of that imagination of increasing a "powertower". After that, to use the letter "h" as its default shortcut/variable is again natural. For instance in the "tetration-forum" (founded at 2007) the term "height" has become a much common use.
(By this I consequently don't like/use the term "super-log()" or "slog()" for the function which tells us the required height of iteration from one $z_0$ to $z_h$ but use simply $text{hgh}()$ as that function in article and software)
disclaimer: this is only amateur-mathematics, no journal-publication or academic practice behind this
Additional remark: in a comment, if I recall correctly, there was a discussion whether exponentiation should be seen as "iterated multiplication" at all (as well as in its generalized to fractional iteration-"heights") but as a genuine operation (I think it was MSE/MO-user Qiaochu Yuan) and similarly for tetration, if at all, should also a more genuine operation be formulated - apart from the basic idea of iteration of an exponentiation. I like this idea much, but such a genuine operation has not been formulated yet. If it is formulated then the term height might be replaced by some more appropriate name - but I don't see any ansatz for this so far...
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
$endgroup$
add a comment |
$begingroup$
When I first (ca 2007) came in contact with (what I later called) "exponentialtower" and which is even in its un-generalized form commonly called "tetration", this occured under the name "powertower" (for instance see mathworld). It seemed very natural for me to use the term (iteration-) "height" for the extend of iteration of that imagination of increasing a "powertower". After that, to use the letter "h" as its default shortcut/variable is again natural. For instance in the "tetration-forum" (founded at 2007) the term "height" has become a much common use.
(By this I consequently don't like/use the term "super-log()" or "slog()" for the function which tells us the required height of iteration from one $z_0$ to $z_h$ but use simply $text{hgh}()$ as that function in article and software)
disclaimer: this is only amateur-mathematics, no journal-publication or academic practice behind this
Additional remark: in a comment, if I recall correctly, there was a discussion whether exponentiation should be seen as "iterated multiplication" at all (as well as in its generalized to fractional iteration-"heights") but as a genuine operation (I think it was MSE/MO-user Qiaochu Yuan) and similarly for tetration, if at all, should also a more genuine operation be formulated - apart from the basic idea of iteration of an exponentiation. I like this idea much, but such a genuine operation has not been formulated yet. If it is formulated then the term height might be replaced by some more appropriate name - but I don't see any ansatz for this so far...
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
$endgroup$
When I first (ca 2007) came in contact with (what I later called) "exponentialtower" and which is even in its un-generalized form commonly called "tetration", this occured under the name "powertower" (for instance see mathworld). It seemed very natural for me to use the term (iteration-) "height" for the extend of iteration of that imagination of increasing a "powertower". After that, to use the letter "h" as its default shortcut/variable is again natural. For instance in the "tetration-forum" (founded at 2007) the term "height" has become a much common use.
(By this I consequently don't like/use the term "super-log()" or "slog()" for the function which tells us the required height of iteration from one $z_0$ to $z_h$ but use simply $text{hgh}()$ as that function in article and software)
disclaimer: this is only amateur-mathematics, no journal-publication or academic practice behind this
Additional remark: in a comment, if I recall correctly, there was a discussion whether exponentiation should be seen as "iterated multiplication" at all (as well as in its generalized to fractional iteration-"heights") but as a genuine operation (I think it was MSE/MO-user Qiaochu Yuan) and similarly for tetration, if at all, should also a more genuine operation be formulated - apart from the basic idea of iteration of an exponentiation. I like this idea much, but such a genuine operation has not been formulated yet. If it is formulated then the term height might be replaced by some more appropriate name - but I don't see any ansatz for this so far...
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
edited Dec 15 '18 at 11:49
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
answered Dec 15 '18 at 8:58
Gottfried HelmsGottfried Helms
23.4k24599
23.4k24599
add a comment |
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$begingroup$
Not sure people care too much about this. Why do you need this? Perhaps just adopt a word and go with it.
$endgroup$
– Pedro Tamaroff♦
Dec 13 '18 at 14:51
1
$begingroup$
See Tetration : "The parameter $a$ may be called the base-parameter, while the parameter $n$ may be called the height-parameter."
$endgroup$
– Mauro ALLEGRANZA
Dec 13 '18 at 14:53
1
$begingroup$
@PedroTamaroff I don't need it, I find nomenclature itself interesting.
$endgroup$
– Griffin
Dec 13 '18 at 14:57
$begingroup$
@MauroALLEGRANZA You are clearly a better reader than I. Happy to accept as an answer if you make it one.
$endgroup$
– Griffin
Dec 13 '18 at 14:58
$begingroup$
FYI, I've called it the tetrated exponent in some early 2000s sci.math posts.
$endgroup$
– Dave L. Renfro
Dec 13 '18 at 14:59