# Do we have to use ordinals with largest/smallest?

In every-day language, I would say, "Give me the fifth largest pumpkin you have"; that is I would use the ordinal.

However, this feels clunky in mathematical texts, especially when reading out loud: "select the k-th largest element" or, even worse, "the k plus first/oneth largest element".

Is it fair to say/write "the k-largest element"? It seems to me that the "aspect of ordinality" is sufficiently expressed by the -st suffix in larger (or smallest, heaviest, ...), that is the superlative.

• Note that there is a typographic dimension here, too; $k$th largest just looks weird, whereas $k$-largest (do we want/need the hyphen?) works. Commented Mar 23, 2015 at 12:23
• Note that MathJax doesn't work on ELU. However kth-largest is probably acceptable. You may need a hairspace between k and "th". Commented Mar 23, 2015 at 12:29
• k-th largest is acceptable. But this is probably better answered by those in that mathematical specialty. See math.stackexchange.com Commented Mar 23, 2015 at 12:44
• @AndrewLeach I know, that's why I used code formatting. ;) The looks of mixing the math font (italic) with text (upright) specifically annoys me, so I'm trying to avoid that. Commented Mar 23, 2015 at 12:49
• I was suggesting that the better judges of acceptability would be the experts in mathematical English, rather than those here. You'd get any 'what I prefer' here as well as there equally. Use "the $k$-th largest element", not $k$ largest, that's how it is said. Commented Mar 23, 2015 at 12:56

Consider this situation where you could write your request as

Give me the 5th largest sheep

or

Give me the 5 largest sheep

They obviously mean completely different things. One will result in you having a sheep, the other in you having five sheep. Hence you should stick to the kth convention.

• Of course you pick a deliberately confusing example. The use case I have in mind is with the proper noun "element(s)" (no confusion), and all other use cases in my context I can imagine are unproblematic as well. Also, my proposal was "5-largest", not "5 largest" (I think the difference is crucial, for the reasons you state). Note furthermore that it won't be kth but k th, and I state that the mixture of fonts is one of the reason of my asking. So in all, thanks, but this does not help me. :/ Commented Mar 23, 2015 at 16:24
• The mixture of fonts is not mentioned in your question. In addition, the "aspect of ordinality" is not sufficiently expressed by means of the superlative, as it took me about 2 seconds to think of an example that would break your attempt at creating a new convention. Mathematicians are perfectly happy saying things like "kth" and "k-plus-oneth" simply because they are unambiguous. Mathematicians deliberately eschew ambiguity, hence I repeat that you should not try to create a new convention. Incidentally, "kth" is perfectly fine too, as far as the mathematician in me is concerned. Commented Mar 23, 2015 at 16:37
• Another option is to use "n" instead of "*k"", as you will find that "nth" is well used, and even documented in English dictionaries, as well as mathematical glossaries. Commented Mar 23, 2015 at 16:40