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What is “unnecessary” in language? There’s a lot in language that is redundant, logically self-contradictory, or superfluous. Language is not logical; it’s not scientific.
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It directly contradicts your “4th of July” construction. If “July 4th” is unnecessary, then so is “4th of July.” As I said before all these things are essentially abbreviations of the phrase “fourth day of the month of July” – you can write it as “4th of July,” “July 4th,” “4 July,” “July 4,” among other ways. They all mean exactly the same thing and, moreover, “4th of July” and “4 July” are commonly pronounced exactly the same way – “the fourth of July.” In German, they often even go ahead and put in a period – “4. Juli” – to direct your attention to the fact that’s an ordinal number there.
I’d say anything that’s redundant, logically self-contradictory or superfluous.
See? We agree on that, at least…
Hari Seldon , mathematicians often talk about the nth iteration or whatever, so it does not sound weird to me to talk about the “n plus oneth”. YMMV.
If you are going to insist that there is a correct and incorrect version of English, then you have to pick a set of rules that already exists. And no set of rules says to use “July 4th, 2011.” “July 4, 2011,” is actually pronounced the exact same way. (I am unsure how you would indicate that someone mispronounced it as “July four” without writing out the word.)
While, countries that actually use “4 July 2011” as their default date notation may pronounce it “Fourth of July 2011,” we Americans generally don’t. The most obvious example is when we refer to the holiday, and while we spell it out as “Fourth of July,” we do use the ordinal.
I don’t know why people insist that the rules must have a logical basis. The rules are just observations of pre-existing style choices. There is nothing inherently logical about them.
I’d say you see the numeral-plus*-th/-rd*/etc. format less often in dates than in instances where a sesquipedalian number requires ordinalization in a sentence. For example, “The minister then said, ‘Let us now recite the 121st psalm’.” The written-out-form “one hundred twenty-first” is awkward; leaving off the “-st” means you read that as “one hundred twenty one” and go “huh?” when it turns out to be ordinal, and writing it as “Psalm 121” would be read as “psalm one hundred twenty-one”, which is not what he said.
To elaborate on what I said before, I would pronounce “n+1” as “n plus one”. I would not say “n plus first”, I would say “n plus oneth”, so I would write that as “n+1th”, not “n+1st”.
YMMV.
So would I. “n + 1st” makes me think I’m adding an ordinal to a cardinal, while what I want is “(n+1)th”.
All I can say is that it sounds weird to me and I have used n+1st in published papers and no referee ever objected.