Mathematicians commonly have to form ordinals from variables: you might look at the kth element of a sequence, for example. When the variable is a single letter, the ordinal is always formed with the suffix -th. Thanks to the unwritten conventions of variable naming, this usually results in one of the easily pronounceable words ith "eyeth" jth "jayth" kth "kayth" nth "enth" or mth "emth".
Things get a little bit trickier when you look at the elements near the kth one. Two opposing forces drag you in different directions when you try to form the ordinal for (k+1). On the one hand, orthographic consistency favours (k+1)th; on the other hand, "kay plus oneth" sounds less natural out loud than "kay plus first". In fact, I've caught one of my professors in a lecture saying (k+1)st at the exact same time as he was writing it on the board — as (k+1)th.
I think both variants are in use, and each has a defensible argument behind it, so I don't think one or the other is "correct". But I wonder if one gets used more than another. Ideally, I'd like to know
Between (k+1)th and (k+1)st, is one used more often than the other?
and better yet
Does usage differ based on context?
(I'm mainly curious about written vs spoken contexts, but I imagine it could be different based on discipline. Mathematicians can't be the only ones with this problem...)
Those are the questions I'd like to answer, anyways. I fear it might not be definitively answerable (although anecdotal evidence is still welcome!). My usual method — count the Google hits for each variant — is useless here because of the way Google handles punctuation. So, as a side note, I'd also love to hear answers to the more general question: How do I determine how widely used a term is when it consists mostly of punctuation?
I thought I should clarify that the motivation for this question doesn't come from a particular instance I had in mind: I typically say (k+1)st out loud but might lean towards (k+1)th if I ever had to write it. I'm mostly curious about how they're used by others. I appreciate all the data points in your answers and the parallel Math.SE question!
It seems that some of you have shared my Google troubles when trying to measure the relative usage of (k+1)st and (k+1)th.
I realized that the underlying issue is applicable to more common usage problems, so I've spun the last part off as a separate question: see Compare usage between punctuation variants. Whoops, looks like that was a bit too meta as a separate question. So just keep in mind that Google page counts seem to be unreliable for this particular question unless you find a workaround to make it search for punctuation properly.
Anyone who can get some sort of tool to find hard data on this question gets an invisible second upvote from me and my eternal gratitude :)