# i-th vs. iᵗʰ vs. ith

I wonder which form(s) are correct amongst the following:

• This is the i-th item in the sequence.
• This is the ith item in the sequence.
• This is the ith item in the sequence.

Example:

From Finlayson, Bruce A. Numerical methods for problems with moving fronts. Bruce Alan Finlayson, 1992.

A related discussion on LaTeX Stack Exchange: 1st, 2nd and i-th?

• I've never seen the first one but I've seen plenty of the other two.
– J.R.
Dec 31, 2015 at 17:02
• Hmmm. Interesting. This looks like a special case because "ith" would look odd in writing... so to specifically clarify and make it obvious that it's a variable, the hyphen is used - "i-th" But, in general, I do not believe this form would be used. The more common use for an undefined term is "nth"... which won't be confused with anything else, generally. Dec 31, 2015 at 17:30
• @Catija Thanks, is there any reason why `nth` would be preferable over `iᵗʰ`? Dec 31, 2015 at 17:32
• I suppose that if you italicize "ith" instead of superscripting it, that might make it more obvious and look less like a typographical error. Dec 31, 2015 at 17:41
• Here's a related question on ELU: Do I write p-th or pth? Dec 31, 2015 at 22:10

The problem occurs because some display devices do not support superscripting (9th) or multiple fonts (9 th). From my experience:

When the th is preceeded by a numeric, there is no problem

4th
120th

this form is often used in addresses in the US.

For a number as text the th is considered part of the text

fourth
ninth
eighth

When a counting variable is used, a "-"(hyphen) can be added for clarity

i-th
j-th
n-th

[ Note: i and j are used in standard mathematical matrix notation ]

When a specific iteration is referenced, a hyphen is also used

9-th
20-th

to maintain conformity.

[ Note: this is different than the first example ]

• Can you offer a citation for your claim that a hyphen is usually used? My personal experience with textbooks and academic papers (for mathematics specifically) is that a hyphen is not common.
– Era
Jan 6, 2016 at 17:34

As far as I know, there is no firmly established standard for writing this kind of "numbering". Best practices are determined by the common usage within the relevant field (e.g. math, physics). Mathematical notation (which this is) is always a matter of convention and can vary even between subfields.

The third option is by far the clearest in the case of the given example, but I can also imagine ith being acceptable. nth is common enough not to require the superscript. You might want to use the hyphen for, e.g., variables that already have subscripts and/or superscripts. The example of i-th you gave looks unusual to me, but the fact that it exists in a recent publication suggests that it is also at least somewhat acceptable.