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