In discussing a merge request related related to sc0ttman's package, I realized that I had a mathematical concept in mind but couldn't recall the precise terminology but after some brief googling, perhaps I never learned the precise terminology!
The idea here is that you can combine two variables into a single variable. To make it obvious you can separate the value of each variable by a comma, in which case the combined value is like an ordered pair [1], which mathematically has a lot of similarities to both vectors [2] and tuples [3].
Survery of related concepts
Anyway, the value of of a given combination or multiple variables doesn't need to be as obvious as a comma separated list as long as there is a one to one relation [4] between said value and the ordered pair [1]. Also if said one to one relation exists than the function (or relation [6]) is invertible [5].
Anyway, I'm 99.9% sure the concept I was looking for is called the "Cartesian Product" [7], but said concept is one of those things which you see defined in it's own right and in relation to other definitions but never really the primary focus of discussion(, unless you are a graduate level mathematics student?). The idea of the Cartesian product perhaps also lacks generality, in that all combinations of ordered pairs in the two sets forming the Cartesian product are included. This is why it is also called the "Rectangular Product" and structure wise has a lot of resemblence to things like the cross product [9], outer product [10], exterior product [11][12][13] and external product [14].
Summary
Anyway, I think the simplest mathamatical terminaology is:
1. The space of possible combined values is called the Cartesian product, although some combination may be invalid.
2. If you represent all possible combined values in a matrix format what you construct is called an "Outer Product"
What to discuss in this thread
Please feel free to discuss any of these concepts in this thread at what level level of mathamatics that you like. since this is not a math forum and we all have different backgrounds (levels of skill) in mathamatics).
Notes for the pedantic
In past Usenet discussions some posters like to show their level of academic ability by focusing on the distinctions and if you aren't precise they will shoot you down hard. My brain likes to see the similarities between things and I think that there is a degree of subjectivity to this. If by ones subjective understanding two things aren't similar well good for you I guess. The intent of this thread isn't to show how mart one is.
This doc is partially in draft state
I have to leave somewhere so I'll need to re-read this post and edit it a bit better. Hopefully it is clear as is
Notes
1 - https://en.wikipedia.org/wiki/Ordered_pair
2 - https://en.wikipedia.org/wiki/Vector
3 - https://en.wikipedia.org/wiki/Tuple#Tup ... ered_pairs
4 - https://en.wikipedia.org/wiki/Injective_function
5 - https://en.wikipedia.org/wiki/Inverse_function
6 - https://en.wikipedia.org/wiki/Heterogeneous_relation
7 - https://en.wikipedia.org/wiki/Cartesian_product
9 - https://en.wikipedia.org/wiki/Cross_product
10 - https://en.wikipedia.org/wiki/Outer_product
11 - https://en.wikipedia.org/w/index.php?ti ... x_notation
12 - https://en.wikipedia.org/w/index.php?ti ... or_product
13 - https://en.wikipedia.org/w/index.php?ti ... r_products
14 - https://en.wikipedia.org/w/index.php?ti ... =898881137
15 - https://en.wikipedia.org/w/index.php?ti ... or_product
16 - Hogben, L, ed. (2007). Handbook of Linear Algebra.[page needed] -- This might be the link: http://www2.fiit.stuba.sk/~kvasnicka/Qu ... 007%29.pdf See page 13-13.
