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Consider the alphabet (ABC...XYZ). The order is defined, but meaningless.

Say we have a subset of letters: BEKOPX

How can I say that ‘B’ is the “first-est ” and ‘X’ is the “last-est” occurring letter in this given set? Not because of their positions in this set, but because of their positions in the original alphabet.

Edit:

Consider different-sized photos in an old scrapbook. They have dates on them, but they were not added to the album in strict chronological order. Still, they appear in sequence as you flip through the pages.

"Earliest", "alphabetically earliest", "nearest", "smallest", "least", etc. may work most of the time because there are enough of these words to choose from to avoid confusion when a conflict arises.

The scrapbook example illustrates a few conflicts all at once.

  • I take it that you want a generic way of doing this, so alphabetically, chronologically, and similar domain specific terms are ruled out? If yes, is the reader expected to be able to order the set intuitively, or from a previous definition, or are you just now in the process of telling him which is first (is this new information)? – Phil Sweet Dec 25 '18 at 1:11
  • Some terminology - totalordered(see especially under chain), partialordered, wellordered, wellfound. Your first task is to classify the ordering type that is relevant to the target set. Then use the terminology that is available for that type of ordering. If the set has an alphabet-like chain ordering, it is wellordered. It has a least element and a greatest element. – Phil Sweet Dec 25 '18 at 1:48
  • Thanks @PhilSweet. I'm now in the rabbit hole... Yes, I'm looking for generic words used in linear sequences. The reader knows what "before" and "after" means for the given sequence (no new information). Still "least" and "greatest" refer to size and potentially other things aside from the linear ordering per se. – Marin Dec 25 '18 at 11:18
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Simply use the words "first" and "last" but use more words to define the order. Alphabetical order is well enough defined. For example:

If we arrange the names of the Disney seven dwarves alphabetically, Bashful is first and Sneezy is last.

When the planets of the solar system are arranged in reverse alphabetical order, Venus comes first and Earth is last.

  • Actually, your statement about the Seven Dwarfs is wrong.  Also, see Ngrams, Tolkien1 and Tolkien2. – Scott Dec 24 '18 at 19:29
  • Thanks @Scott. I’ve corrected it. Also, I did pause before using "dwarves". The links are informative, and, given that Snow White probably predates Tolkien, "dwarfs" is probably the correct spelling, but I’ve left it as it is for now. – Pam Dec 24 '18 at 20:39
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I would say "Alphabetically earliest" or "Earliest in the alphabet".

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There are two possibilities here.

  1. You are faced with multiple ordering ideas on the same set. This rarely is a problem because people are pretty good at juggling this and there are quite a few unique lexicons for the most commonly encountered orderings. If a have a list of historical events, It is easy to talk about them in chronological order, or geographically, or based on significant influence on a later time. You don't often need to explicitly name the ordering because the metric words are specific to each type of ordering.

  2. The scrapbook problem is a bit different. Let's say you visited all the capitals of Europe. And in each one, you bought a postcard that depicts some dated historical event. Your grand-kid decided to build a house of cards and took them all out of the scrapbook. Originally, the cards appeared in the scrapbook in the order you visited the cities. Each card has two date attributes, the date you visited and the date of the event depicted on the card. You have a single ordering (dates) applied to two different sets (visit dates, depiction dates), and there is a physical one-to-one correspondence between the sets. You can't rely on the lexicon to help you here. You have to tell us which set the ordering is being applied to. You have to identify the different sets, name them, and explain the relationships between them in the beginning before you can expect the audience to follow what's going on. You can't unambiguously talk about ordering the cards datewise. You have to talk about the actual sets that are being ordered - visit dates or depiction dates. Now once you've done all the necessary prep work, you can use the the typical descriptors for that ordering. For abstract mathematical orderings, least element to greatest element is used.

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