“Sequential Order” is a fantastically important aspect of our core cognition and processing.
It supports accelerated “Searching” and “Finding”; for instance a Library stores its volumes, generically, in Alphabetic Order of Author, so that you can readily FIND books by a particular author, without having to start at one end of the effective “bookshelf” and work through the books, which would in the absence of this concept NOT be stored in an alphabetic way.
So it would be a bit of a lottery as to how long it took to find a particular book by a particular author.
Integers are the most obvious realisation of Sequential Order, but they are NOT its definition; Sequential Order has its cognitive roots in Physical Order.
Here is an existing conventional numerical realisation of Sequential Order:
1, 2, 3, 4, 5, 6, 7, 8, 9
Here is an alternative numerical realisation of Sequential Order:
1, 2, 7, 4, 5, 6, 3, 8, 9
If I were in some way to DEFINE that the second set was hereafter to be used, Canute-like, then most computer systems would fail, and have to be re-written.
Another well known Sequential Order is:
a, b, c, d, e…..etc
I could DEFINE the Sequential Order to use in an application whose Subrelations I am currently designing as:
MHJ, FCT, IAR,TQT, BCH, KQF,……
since this is the “Physical and Visible” Sequential Order in which a population 0f system-unique 3 upshifted alpha character strings, which are the population of Identifiers within this system, are actually located in the “Identifiers Allocation Subrelation”.
P.S. I note that the underlying electronics of this website only allow the re-ordering of menu items in a menu by actually physically re-ordering items on a screen; you don’t, for instance, allocate numbers to determine position.
You click and hold on a menu item, and move it to the desired place in Sequential Order.
I rest my case, M’Lud.