On May 4, 2020, at 10:44, Steve Barnes GadgetSteve@live.co.uk wrote:
And "equal" doesn't say what it's equal.
What we need is a word that means "same length", much as "shorter" and "longer" are about length.
There's "coextensive", but that'll probably get a -1.
If “equal” is bad, “coextensive” is much worse. “Equal” is arguably ambiguous between “same length” and “same values”, but “coextensive” usually means “same values”.
“The County shall be coextensive with the City of San Francisco” doesn’t mean that it’s 49.81 square miles, it means it consists of the exact same 49.81 square miles as the city. “The golden age of Dutch culture was roughly coextensive with the Netherlands’ reign as a world power…” doesn’t mean it was roughly 67 years, it means it was roughly the same 67 years from 1585 to 1652.[1] “Consciousness and knowledge are coextensive” means that you know the things you’re conscious of. And in math[2], a popular example in undergrad textbooks[3] is that (Z/7Z, +) and (Z/7Z, *) are coextensive but still distinct groups. The most popular formulation of the axiom of reducibility in early predicative set theory was “to each propositional function there corresponds a coextensive predicative function”. Even in measure theory, it seems to always mean “same extension”, not “same extent”.
So, this would be a great name for the function in the other thread about comparing lists and tuples as equal, but it’s not a great name here.
Some dictionaries do give “commensurate” or similar as a secondary[4] meaning, but at best that would mean it’s still ambiguous.
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[1] And here I thought it was 1989 until whenever Guido left.
[2] I didn’t even remember that it was used in math until I used the word in its normal English sense and one of the other Steves accused me or resorting to mathematical jargon—but after that, I did some searching, and I was wrong, and it actually is reasonably common.
[3] Seriously, I found the exact same example in three apparently unrelated textbooks. Which is pretty odd.
[4] Or even later, after giving the same spatial boundaries, then the same temporal boundaries, then the math/logic definition, but I’m lumping those all together as one sense because they’re coextensive if spacetime Is topological. :)