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Is there an adjective to mean "sequential in ascending order" regardless of object type (word or number)? I need the word to imply "alphabetical" if the object is a word; or "numerical" if the object is a number.

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Do you mean, a set of values that which could be sorted, because they have a kind of common-sense ordering, or a set which is in the sorted order already, right now? –  Warren P Apr 25 '11 at 23:47
    
@Warren, I mean values that can be sorted (and where duplicates are possible), such as a set of names or random numbers. –  superuser Apr 26 '11 at 3:12

5 Answers 5

up vote 3 down vote accepted

"Collated" is a more general term that encompasses both alphabetical and numeric sorting.

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The term sorted seems to cover both alphabetic and numeric.

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To me something is sorted, if you put it into order. But it doesn't mean "the entities in question have the property of being sortable". –  Warren P Apr 25 '11 at 23:43

"Enumerated" or "ordinal" come to mind.

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If sorted isn’t the word you’re looking for, maybe consecutive is.

Sorted just means they’re in order; consecutive means “following, in succession, without interruption” (Wiktionary).

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3  
Consecutive means, nothing missing. consecutive years would mean, for example 1977, 1978, 1979 without skipping any years. Something could be ordered, but missing some years, and that would be sortable, but not complete. So in this case, consecutive doesn't fit. –  Warren P Apr 25 '11 at 23:44
    
@Warren P: That is one of the things the word "sequential" in the question can mean. –  Jason Orendorff Apr 26 '11 at 14:13

Math people would speak of something being "well-ordered", and it's an adjective, but it's two words in common usage.

A set of values is well-ordered, if it has a least element, a greatest element, and all the elements in between have exactly one proper sorted position within that list. "Integers between 0 and 10" is a well-ordered finite set, for example. A set of symbols A,B,C,D where A=1, B and C both equal 2, and D=3 are NOT well ordered, because there is no way to decide whether B or C comes first. Infinite sized sets such as "all positive and negative Integers" are not considered formally "well ordered" because there is no "least element" or "greatest element".

If you are going to refer to finite sets of symbols, letters, and numbers, I would say "well-ordered", and I would speak of sets of those symbols being well-ordered.

Sometimes math people leave the dash out (Wellordered). Well-ordered in Merriam Webster dictionary is two words, but in some math papers it's one.

If your readers are not math-people you might find it valuable to use this term, and define it for them. If using a term your readers don't know, and definining it isn't possible, I'd use a long sentence description, and a close-enough-for-rock-and-roll word like Sortable. "These things that can be sorted, easily into exactly one order, I will call for our purposes, Sortable"

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+1 for an interesting math view. My readers aren't math people, and in fact, they prefer sentences nice and short. Unfortunately, "well-ordered" might be too mathematical and perhaps overly complicated for my purposes. –  superuser Apr 26 '11 at 3:27
    
Not quite so. A set is well-ordered if every non-empty subset has a lest element, so the definition does not require a greatest element. The set of natural numbers is well-ordered even if it doesn't have a greatest element. I'm a math guy... –  Theta30 Aug 23 '11 at 17:36

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