# Is it correct to say -1th or -1st?

I like to say -1 as negative one. So, should I say "negative oneth index" or "negative first index"? Which one is grammatical?

Is there a way to avoid this problem altogether.

• I don't see any reason to say "negative oneth." It seems to me that adding "negative" before "one" wouldn't change things any more than adding "twenty" before it, and we still say "twenty-first" and not "twenty-oneth." Commented May 19, 2016 at 3:07
• Related question: (k+1)th or (k+1)st? Commented May 19, 2016 at 3:43
• @sumelic That's probably because there are no such ordinals as oneth, twoth, threeth to parallel the adverbs once, twice, thrice.
– tchrist
Commented May 19, 2016 at 4:04
• @tchrist whence the expectation that ordinals would relate to adverbs? Commented May 19, 2016 at 4:35
• Related: Ordinal form of negative numbers (especially -1, -2, -3) [closed] english.stackexchange.com/q/309713/14666
– Kris
Commented May 19, 2016 at 5:57

Should I say "negative oneth index" or "negative first index"?

You should say neither.

Which one is grammatically correct?

Neither is correct usage. They're probably grammatically correct in the way that "very unique milk" is gramatically correct even though it is so wrong in so many ways.

Is there a way to avoid this problem altogether.

Yes, say item negative one or index negative one.

You shouldn't be using ordinals for indexes. The item at index zero in a c-style array is the first item in the array. It's not the zeroth item, though you can call it item number zero.

Ordinals only make sense as an outgrowth of natural numbers. That's why zeroth and negative- anything sound so bizarre.

• -1 That's not the question, though. So, this is a good comment but not an answer.
– Kris
Commented May 19, 2016 at 5:48
• @Kris the question ends with "is there a way to avoid this problem altogether," and my answer addresses that. In the course of addressing it, I also answer by implication the questions in the first paragraph, the answer being "neither." I will edit to make that explicit. Commented May 19, 2016 at 6:29
• @Kris the question is one that assumes the answer. A reasonable response, like this one, states there is no such direct answer. Commented May 19, 2016 at 12:40
• Maybe there is a morphological gap here, but it's not true that there is no logical use for ordinal forms of non-natural numbers in English. People use ordinal forms for many purposes. One use is to denote exponentiation, as in "two to the second power," and the function of exponentiation is defined for negative numbers. Something like "two to the negative first/oneth power" makes perfect sense mathematically and syntactically, it just sounds odd. (There is also a work-around here, of course, in "two to the power of negative/minus one.") Commented May 19, 2016 at 18:01

It is minus-oneth index.

See "oneth" on Wiktionary en.wiktionary.org/wiki/oneth

(archaic, nonstandard) 'first', or other ordinal derivatives of 'one', such as hundred-and-oneth or minus-oneth

Usage:

Perhaps the following thoughts may be useful. They concern the "minus-oneth" law of thermodynamics, a presupposition of the subject, that for a system, there exist states of internal thermodynamic equilibrium.

An Earlier Year from The Oxford Magazine, Noughth Week, Michaelmas Term, 1996, p.4.

Undergraduates are keen to come up before the beginning of term, but are already flown by tutorial time in Eighth Week. Noughth Week is fuller than Full Term, and now many university committees summon themselves in Minus Oneth Week, which, although a serious loss to scholarly activity, has at last enriched the English language with a rhyme for `month'. (emphasis added)

Comment:
While I was familiar with the usage, esp., in "Minus-Oneth Law of Thermodynamics," I looked up the Wikctionary entry and other references only now.

• What happens next? Minus tooth ? Commented May 19, 2016 at 6:29
• The problem with your argument is that Google actually returns far more hits for "minus first" than it does for "minus oneth." This discrepancy holds if you search for the exact phrases "minus oneth law of thermodynamics" and "minus first law of thermodynamics." Commented May 19, 2016 at 6:37

I've never heard anyone say "oneth". Intuitively it sounds very strange to a native's ears. I'd stick with "negative first" or you could say "the first negative index".