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Raising a number to a non-integer power.

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TimFox:
English terms for mathematical concepts are usually existing words, already in use in common language.
"Function" (v) can mean to work or operate in a desired way
"Function" (n) can refer to a formal social event.
The advantage of using "standard" nomenclature is the ease of locating information, as in the Wikipedia article on "distribution".  I like Wikipedia's term "disambiguation" for separating out different meanings of the same word.

Nominal Animal:
I wasn't disagreeing, just trying to make sure others reading this thread won't accidentally conflate it with statistics, TimFox.

In this kind of a thread, where we're looking at ways to help others understand stuff better, I've found that carefully picking the terms to help steer those climbing the ladder helps, even if the terms used aren't the conventional or usual ones; the implicit associations matter.

I do agree that distribution is the better term, in general.  But, in the context of this particular thread, the underlying key is extension or generalization of mathematical tools we have real world analogs for to those we have not.

As an example, when talking about unit quaternions in the context of spatial rotations, I like to use the term versor, because many (programmers at least) have encountered quaternions and found them untractable or unreasonably hard.  The truth is, unit quaternions are easy, much easier than Euler or Tait-Bryan angles, and perfectly useful for anyone working in 3D on computers or microcontrollers.  In the realm of spatial rotations, versors really only use a couple of details from quaternions proper (Hamilton product, really).  Slap on conversion to a 3D rotation matrix (of which there is only one, unlike Euler or Tait-Bryan angle conventions), addition/interpolation properties (and how renormalization to unit quaternion does not have any directional bias, unlike E/T-B), plus possibly recovering the versor from a pure 3D rotation matrix, and it's all there.  It all fits one one or two sheets of paper.  Picking the name "versor" is just a psychological tool to avoid the association with any preconceptions on how quaternions are "hard".  Since they haven't any preconceptions against "versor", they tend to be very surprised how simple the operations and their implementation are.

basinstreetdesign:

--- Quote from: daqq on May 27, 2020, 08:18:44 pm ---
--- Quote from: T3sl4co1l on May 27, 2020, 03:17:43 pm ---
--- Quote from: mark03 on May 27, 2020, 03:12:31 pm ---What is this number i that you speak of?

--- End quote ---

You must be 'j'oking ;D

Tim

--- End quote ---
He probably just imagined it.

--- End quote ---

Get real! ;D

RoGeorge:

--- Quote from: basinstreetdesign on May 31, 2020, 02:17:37 am ---
--- Quote from: daqq on May 27, 2020, 08:18:44 pm ---
--- Quote from: T3sl4co1l on May 27, 2020, 03:17:43 pm ---
--- Quote from: mark03 on May 27, 2020, 03:12:31 pm ---What is this number i that you speak of?

--- End quote ---

You must be 'j'oking ;D

Tim

--- End quote ---
He probably just imagined it.

--- End quote ---

Get real! ;D

--- End quote ---

That's not natural!   ;D

Brumby:

--- Quote from: RoGeorge on May 31, 2020, 06:43:46 am ---
--- Quote from: basinstreetdesign on May 31, 2020, 02:17:37 am ---
--- Quote from: daqq on May 27, 2020, 08:18:44 pm ---
--- Quote from: T3sl4co1l on May 27, 2020, 03:17:43 pm ---
--- Quote from: mark03 on May 27, 2020, 03:12:31 pm ---What is this number i that you speak of?

--- End quote ---

You must be 'j'oking ;D

Tim

--- End quote ---
He probably just imagined it.

--- End quote ---

Get real! ;D

--- End quote ---

That's not natural!   ;D

--- End quote ---

 :palm:

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