changing terminology (was: overview paper co-author invitation)

[andydude]

OK, so lets take a poll (all entries are short terms for the forms: superfunction of \( f \), Abel function of \( f \)):

1. \( f \)-exponential, \( f \)-logarithm
   
2. super-\( f \), sub-\( f \) (with recognized misuse of "sub")
   
3. super-\( f \), Abel-\( f \) (with recognized ambiguity of "super")
   
4. iter-\( f \), Abel-\( f \) (sorry about the Fatou joke)
   
5. iter-\( f \), itra-\( f \) (by analogy to "inter" and "intra")
   
6. ultra-\( f \), infra-\( f \)
   
7. meta-\( f \), para-\( f \)
   
8. super-\( f \), antisuper-\( f \)
   
9. super-\( f \), arcsuper-\( f \)
   

I will vote last, to promote unbiased votes. You can vote for at most 3, but please say which one you prefer, for example: A first, G second.

[bo198214]

OK, so lets take a poll (all entries are short terms for the forms: superfunction of \( f \), Abel function of \( f \)):

1. \( f \)-exponential, \( f \)-logarithm
   
2. super-\( f \), sub-\( f \) (with recognized misuse of "sub")
   
3. super-\( f \), Abel-\( f \) (with recognized ambiguity of "super")
   
4. iter-\( f \), Abel-\( f \) (sorry about the Fatou joke)
   
5. iter-\( f \), itra-\( f \) (by analogy to "inter" and "intra")
   
6. ultra-\( f \), infra-\( f \)
   
7. meta-\( f \), para-\( f \)
   

Haha, you are biased! Where is the arcsuper-f???
And do you honestly want to keep e.g. Abel-exponential as an option?
And a secret poll would also more democratic.
I also throw "antisuper-f" into the round!

[andydude]

And do you honestly want to keep e.g. Abel-exponential as an option?

No, but that would be voting...

And a secret poll would also more democratic.

Can you do secret polls? I cannot figure out how to do that with this forum...

Where is the arcsuper-f???
...
I also throw "antisuper-f" into the round!

OK, I've appended it to my post.

[bo198214]

Can you do secret polls? I cannot figure out how to do that with this forum...
...
OK, I've appended it to my post.

Tetratophile did the work already for you!

[andydude]

P.S. If you have some Ficial, we can make a SuperFicial for it.
But do not tell economists about our achievements: they deal with Inflation...

LOL! It made me think about the other superfactorial and the superduperfactorial. This conflicts with the super-factorial terminology (as in the superfunction of factorial), because "super" is such a popular prefix. Being a popular prefix, we cannot change its meaning to be more precise in a permanent way. I think the "super" prefix is so general that it cannot be pinned down to a specific meaning, even in the context of a single paper. It is one of those prefixes that does not want to be defined. You may define "superlogarithm" or "superfunction" however you want, because you can still use "super" in front of other words. As long as it stays this way, "super" will continue to add meaning to new words, but as soon as you define "super", then every word that uses it will loose all of its meaning. "Superlatives" will become superfunctions of latives and "Superheroes" will become superfunctions of heroes. It doesn't lead to a nice semantic world. "Super" cannot be tamed; it will always be more than you think it is.

Andrew Robbins

[bo198214]

"Superheroes" will become superfunctions of heroes.

Reminds me of that joke: An operator stands at a bar. Comes a good looking function by. Operator: "Hey baby, shall I properly differentiate you?"
Function: "If you like, but I am \( e^x \) !"
Operator: "But I am \( \frac{\partial}{\partial y} \) !"

Ya well Andrew, your pleading for the free super-world is quite convincing.

[bo198214]

Perhaps also interesting to know that Écalle calls itérateur (iterator) what we call Abel function and he calls pre-itérateur what we call Schröder function. (Imho very misleading naming.)
The Julia function is commonly called iterative logarithm.

[andydude]

@Kouznetsov
So, if we use f-exponential and f-logarithm, then the functions in 2009supefae.pdf would be called:

• FactorialExp (for SuperFactorial)
  
• FactorialLog (for ArcSuperFactorial)
  

... much more concise!

[bo198214]

@Kouznetsov
So, if we use f-exponential and f-logarithm, then the functions in 2009supefae.pdf would be called:

• FactorialExp (for SuperFactorial)
  
• FactorialLog (for ArcSuperFactorial)
  

... much more concise!

I would rather name it !-exponential and !-logarithm, as short form for functional exponential/logarithm of the factorial.

So then the terms super-exponential, super-logarithm and superfunction would still be in effect (?).

[Base-Acid Tetration]

Also please vote in the hyperoperations terminology poll if you are interested.