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The words infimum and supremum are technical terms in mathematics. Should their plurals be infima and suprema or infimums and supremums?

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5 Answers 5

up vote 14 down vote accepted

For mathematicians, the plurals of infimum and supremum are infima and suprema, respectively. Google Ngrams shows that the incorrect plurals infimums and supremums are used roughly equally often (and much less often than the correct plurals), so I don't believe there is actually any asymmetry.

Here is the Google Ngram with the incorrect plurals:enter image description here

They are used so infrequently that they barely show up on an Ngram if you try to compare the usage of the correct and incorrect plurals.

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1  
+1 for the other NGram, showing that the "incorrect" plurals are used but show up as flat lines when put in context of the NGram I used –  simchona Aug 28 '11 at 22:07
    
Inferring from Ngrams is an incorrect conclusion since "suprema/infima" are Latin,Spanish, Italian words. Please browse the books. –  Theta30 Aug 29 '11 at 1:49
    
@Bogdan: that may explain why suprema is twice as common as infima. However, if you just look at the books since 1990, over half of the instances of infima seem to be mathematical, and infimums is still quite uncommon. –  Peter Shor Aug 29 '11 at 2:56
    
Those are the correct plurals for classicists and generally speakers of Latin, I daresay! Mathematicians simply borrowed the words. –  Noldorin Aug 29 '11 at 3:14
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@GEdgar: Maybe I should have said "inferior" rather than "incorrect." But the best plural to use is obviously ...ma. Also note that mathematicians use minimums much less frequently then the general populations. From Ngrams, the ratio of minima to minimums is roughly 6 to 1. On the mathematics/physics preprint server www.arxiv.org, Google shows that the ratio is more like 57 to 1, so for mathematicians, at least, I would argue that minimums is incorrect. –  Peter Shor Aug 31 '11 at 17:30

According to this dictionary of math terms, the plural of infimum is infima. Similarly, the plural of supremum is suprema.

As this NGram shows, suprema and infima are also used more than the plurals formed with an s.

enter image description here

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The already given Ngrams are kind of biased since suprema and infima appear as plurals outside of mathematics. One can argue that this is the plural in general. But more than that, those words also appear in inner Latin, Italian or Spanish texts (ex. Corte Suprema).
I suggest Googling the books on the subject "mathematics" for the period 1950-2010.
The results show:

In conclusion, I wouldn't say supremums, infimums are incorrect, but are less used. You can't go wrong with infima/suprema. Note that Wikipedia math articles, such as this also use infima/suprema.

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Infimum ("the lowest") and supremum ("the highest") are Latin words. For the neutral genus, the plural is given by replacing -um with -a . So I would suggest doing it like the Romans: infima and suprema.

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I was kidding a bit. Yes, they are in usage. –  Konstantin Aug 29 '11 at 1:56

Pluaral of Supremum is Suprema. The Plural of infimum can be either infima or infimums.

Wiktionary does wonders.

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2  
Okay, but how do you know Wiktionary is correct here? It doesn't appear to cite any sources. –  Brennan Vincent Aug 28 '11 at 20:36
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Also, the asymmetry between the two seems implausible. –  Brennan Vincent Aug 28 '11 at 20:36
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@Brennan: For mathematicians, the plurals of infimum and supremum are infima and suprema, respectively. Google Ngrams shows that the incorrect plurals infimums and supremums are used roughly equally often (and much less often than the correct plurals), so I don't believe there is actually any asymmetry. –  Peter Shor Aug 28 '11 at 20:58
    
@Peter: make this an answer so I can accept it :). ngrams is a great tool that I hadn't thought of using. –  Brennan Vincent Aug 28 '11 at 21:09

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