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If we refer to the Minimum of a set of numbers, we mean the lowest number. Min(12, 7, 18) = 7 and Min(5, -8) = -8.

Is there a technical term for the 'number closest to zero'? e.g. where fn(5, -8) = 5 and fn(-5, 8) = -5

Similarly, what would be the opposite be (e.g 'number farthest from zero')?

I am aware that there are two solutions in some situations, e.g. fn(5, -5) and that any application of this would have to bear that in mind. However, this question is just about whether or not there is some existing terminology for this function.

HappyDog
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    "minimum/maximum in absolute value"? ... Alternatively, some use the convention "smaller/larger" for comparing size (vs "lesser/greater" for comparing order on the number line). Under that convention, "smallest" and "largest" would convey the idea you describe. – Blue May 13 '21 at 10:08
  • "distance" or "unsigned distance" – user619894 May 13 '21 at 10:09
  • @Blue I like the term 'absolute minimum'. If a more official/sourced answer doesn't turn up, that's something I would be happy to use. Interestingly, my first thought was Smallest and Largest but they seemed a bit informal which is what prompted me to ask this question. – HappyDog May 13 '21 at 10:14
  • @user619894 "distance" or "unsigned distance" - That just leads me to ask 'distance from what?' It would probably need to be 'minimum distance from zero' in order for it to be clear, which is a bit of a mouthful. – HappyDog May 13 '21 at 10:18
  • how about "size"? – user619894 May 13 '21 at 10:34
  • @HappyDog: "absolute minimum" would be my choice, too; but note that it's sometimes considered synonymous with "global minimum" for functions. (See, eg, this Khan Academy lesson.) ... BTW, although I'm one of the smaller/larger conventioneers, I wouldn't assume this of a reader. Given that I'd expect to define terms anyway, I might go ahead and introduce, say, "$\operatorname{absmin}(a,b)$", explicitly advising the reader not to confuse it with "global minimum". – Blue May 13 '21 at 10:38
  • @HappyDog: If "smallest" and "largest" are too casual, you could always go with "smallimum" and "largimum". Latin suffixes make everything seem formal. ;) – Blue May 13 '21 at 10:42
  • Also the 'magnitude' of a number refers to how far it is from zero. So you can say 'the number with the largest magnitude' and 'the number with the smallest magnitude'. As you noted, these need not be unique, but you can then talk about e.g. an element having minimum magnitude. – Slugger May 13 '21 at 10:48
  • @Blue In the end, I went for one of your suggestions - Absolute Minimum/Maximum, which I think has a good foundation in the mathematical term 'Absolute' whilst also being neatly descriptive in an informal way. If you want to write an answer containing this suggestion then I will accept it. If I don't hear back after a while then I'll write my own answer, so that I can close this question down. Cheers. – HappyDog Jun 22 '21 at 11:36
  • @HappyDog: Darn. I was rooting for smallimum/largimum. :) ... Go ahead and write-up your own answer, so we can throw more reputation points your way. – Blue Jun 22 '21 at 12:00
  • @Blue - Done! (...plus a bit more text so I'm allowed to post the comment) – HappyDog Jun 22 '21 at 15:15

2 Answers2

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For the number closest to 0, smallest absolute value, or smallest norm.

For the one farthest from 0, largest absolute value, or largest norm.

Mister Mak
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  • That sounds promising. Can you cite a source for those being used as formal terms, or are they just some suggestions of your own? – HappyDog May 13 '21 at 10:19
  • My own suggestions. However, the definition of "absolute value" is pretty unambiguous, and I don't think there is any ambiguity from the choice of norm for real numbers, so it seems concise and clear to me. – Mister Mak May 13 '21 at 17:04
  • I didn't pick this answer in the end, but I think - in the absence of anything official - it is a good alternative that some people might prefer. +1 – HappyDog Jun 22 '21 at 15:17
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Note: None of the suggestions in comments or answers include references that indicate that there is an established term for this, so in the absence of anything more official I will be adopting the names described in this answer. I would consider changing my answer if anyone is able to post any alternatives which include appropriate citations.

Thanks to various discussion in the comments, in particular a suggestion from @Blue, I eventually settled on the following terms:

  • Absolute Minimum - In a set of numbers, the number closest to zero, regardless of sign.
  • Absolute Maximum - In a set of numbers, the number furthest from zero, regardless of sign.

These fit with the standard definitions of these terms in the sense that the result is the Minimum (or Maximum) of the Absolute values for each number in the set, and therefore feels like it fits well with standard terminology.

Note that Absolute Minimum is sometimes considered synonymous with the Global Minimum for functions, for example in this Khan Academy lesson. If you are in a situation where this might cause confusion (or in any context where you would expect to define your terms) you should advise the reader that Absolute Minimum should not be confused with Global Minimum.

HappyDog
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