# Correct pronunciation of 'xth' (and workarounds for those who find it a tongue-twister)

This is to some extent a cross-posting from English Language & Usage. How do you pronounce “xth”?

I am asking a slightly different question -- but only slightly.

I was attempting to offer ways of dealing with the difficulty of pronouncing 'xth' as in "Please take note of the xth element in the series." This can be tricky, not only for learners of English but even many native speakers.

It occurred to me that this must be bread and butter to maths educators.

Questions

1. What is the correct/customary pronunciation of 'xth'? (Is it eksth)

2. In general are all such terms pronounced as the letter name followed by a 'th' sound. For example is 'wth' pronounced 'double-youth'? Would 'Δth' be pronounced 'deltuth' etc.

3. What advice do you offer to someone who simply cannot pronounce 'xth' because they find it an impossible tongue-twister. How can they make themselves understood?

• 'Ωth' or 'אth' (or even '(alef+1)th') is even more funny :) Or (alef+1)st? :) – Honza Zidek Nov 2 '15 at 11:31
• @HonzaZidek - I would simply say 'alifth' for that. Not so different from 'fifth'. Still, let's see what the professionals say! – chasly - reinstate Monica Nov 2 '15 at 11:32

For things in a list, in my experience it is very uncommon to have things indexed by letters other than m, n, i, j, k and sometimes r. Letters whose names end in a vowel sound (like i, j, k) and letters whose names end in a glide (like m, n, r) offer most people no particular problems with pronouncing the "-th" construction. This even goes for unusual ones like "wth" which I would pronounce as "double youth".

If I do come across the "-th" construction with letters whose names end in consonants (f, h, s, x, z), I often pronounce them with a small gap between the letter and its "th". So "xth" is "eks..th" and "zth" is "zed..th". Note that it's an actual moment of silence, not a vowel sound, so the "th" is not "eth" or "uth" or "ith", but just the "th" sound all by itself. Think saying "x thin" but just stopping at the "th" without saying the "in". It sounds very strange to my ear to say something like "eksuth".

In many situations, I avoid the "-th" construction altogether and just say "element x", or "interval number i", or "the number at position j". It takes more to say and write, but is unambiguous and perfectly pronounceable.

This is especially true for other situations where you might use a "-th" construction such as powers or fractions - most people I know would avoid the "-th" and use an alternative. For example, instead of "The xth power of 2", say "2 to the power of x"; instead of "two mths", say "two over m". Roots are a different thing and the only natural way I can think to pronounce "$\sqrt[x]{2}$ is "the xth root of 2".

I actually think this is the perfect fuel to talk to students about an often underappreciated aspect of mathematical writing -- reading it aloud. In other disciplines you are encouraged to read your own writing aloud, and I think this is still useful advice for maths. The existence of easy-to-write-but-difficult-to-pronounce constructions might just help students consider the needs of their reader a little.

• When you mention a small gap, is it an instant of complete silence or do you introduce a fleeting extra syllable, i.e by saying something like eksuth? Are both options acceptable in your view? – chasly - reinstate Monica Nov 2 '15 at 12:38
• Edited to be clearer about that. – DavidButlerUofA Nov 2 '15 at 13:19
• I would use "1/x power" or "root of degree x" before I would try pronouncing "xth". I might also circumlocute with "nth root, where n=x". Gerhard "Let Me Finish My Crackers" Paseman, 2015.11.02 – Gerhard Paseman Nov 2 '15 at 18:39
• @GerhardPaseman I like "root of degree x". I've never heard it called the degree, but it makes sense. – DavidButlerUofA Nov 2 '15 at 19:38
• @DavidButlerUofA, it is my neologism (royalty-free! use it as needed), and of course substitute something appropriate for degree as you see fit. Gerhard "Time To Eat More Crackers" Paseman, 2015.11.02 – Gerhard Paseman Nov 2 '15 at 20:55

I'm not a native English speaker, but I typically teach technical topics in English to international students. In this context, in addition to the problem of (my lousy) pronunciation, there is another issue. Many students have no idea that, e.g., the nth element is written in that way: they might not have yet read a technical book in English or that piece of information might not have sunk in. Because of this, hearing "enth", however pronounced, might not trigger any familiar word or symbol.

Therefore:

1. If I can support what I'm saying by writing on the blackboard, I say "en-th", clearly separating the two parts and emphasizing the "th". Meanwhile, I write on the blackboard which element I'm referring to.
2. If I cannot write while speaking, I avoid nth altogether by saying "the element number n" or "the element n".

When using letters as variable ordinary numbers, say the letter and add th. (Example: x=ecksth, b=beeth)

If you don't want to say that, say "take note of the element in the x position in the series"

X would be the vowel in this word. When x is used as a vowel, it is pronounced like the letter z.

So, the correct pronunciation of xth would sound like: zith.

• That appears to make no sense. Please explain how 'x' can be a vowel. The only vowels in English are 'a e i o u'. It is true that 'z' can sometimes be pronounced with a 'z' sound for example in 'xylophone' and a few other words that begin with 'x'. All of those words have a vowel or 'y' as their second letter. The string 'xth' does not contain a vowel. I don't believe there is the slightest evidence that 'xth' would be pronounced 'zith' in the context of mathematics. If you have any such evidence please show it. Thanks. – chasly - reinstate Monica Nov 2 '15 at 21:53