# Adjective to suggest X's being either an “additive” or “multiplicative” function of A and B?

In a non-math context (i.e., where readers would not be expected to know the formal definitions of very advanced mathematical terminology) I am trying to express the relationship between three concepts in a precise way. Here's what I want the reader to know.

• X is some function of A & B
• X is never less than either A or B, individually
• Knowing the precise functional form or relationship is otherwise unimportant.

In fact, the last bullet could be even stronger: it's important not to assume anything else about the relationship. The key thing is that X is at least the greater of A or B. It's never less. It may be A + B. It may be A + only part of B. It may be A * B. It may be A * only part of B. We don't know. So I'm looking for a term that basically means the whole is not less than its parts.

Simply expressing this by saying "X is a multiplicative function of A & B" would impose too many assumptions on functional form, even if by some analysis it's mathematically correct. Writing "X is a multiplicative or additive function of A & B" is better but is cumbersome, still places untoward emphasis on the actual form, and introduces even more technical terminology. In researching this, I have discovered that "arithmetic function" may(?) cover both additive and multiplicative cases but I don't know that it explicitly excludes the possibility that X being less than A or B. Even if so, it is almost certainly too specialized a term.

In any event, the sentence that I'm hung up on currently reads like this: "The total amount of i in X is always some ______ function of the i in A and the i in B."

My questions, then, are: 1) is there an adjective or adjectival phrase that can fill that gap for my purposes; 2) if you think "arithmetic" works, do people actually use and understand it in the way I'd being using it, and; 3) if you don't think it's possible to express this relationship in the form I'm currently imposing, how might you succinctly do so otherwise?

• Is X linear? Is X bounded by A * B? – jxh Feb 24 '17 at 20:30
• Would love to read your thoughts even if conditioned on different answers... but, for both questions, the answer is that we don't know and I specifically want to avoid the appearance of endorsing either assumption. In point of fact, it's probably non-linear and is probably not greater than A * B. – MDHunter Feb 24 '17 at 21:55
• I think you could say: The lower bound of X(i) is the maximum of A(i) and B(i). But, I may be misunderstanding your sample sentence. – jxh Feb 24 '17 at 22:35
• Do you need to express the sentence as "___ function of"? Otherwise, you can just say that X is no smaller than the smaller of A and B (or some less clumsy phrasing thereof). – Lawrence Feb 24 '17 at 23:43
• Quibble. You're changing what X is between 1. and 2. If X is a function of a and b, then 2. should read "X always evaluates to a number greater than either a or b". It is conventional to set both variables and functions in italics. @Lawrence, it should be " [...] than the greater of A or B [...]" – Phil Sweet Feb 25 '17 at 15:36

## 2 Answers

This is a very surgical sentence you're trying to construct. To help cipher it out I used:

• X = a pie
• i = calories
• A = pears
• B = berries

Thus it seems you want to convey: "The total amount of calories in a pie is always some ______ function of the calories in pears and the calories in berries."

To your questions:

1. The adjective I suggest is "compounded" suggesting either additive or multiplicative properties which would mean X is never less than either A or B, individually.
2. I don't think "arithmetic" works. It's too broad and doesn't cover your second condition (X is never less than either A or B, individually).
3. I don't think I could construct a tighter sentence than "The total amount of calories in a pie is always some compounded function of the calories in pears and the calories in berries."
• Upvoted for the creative mad lib. – jxh Feb 24 '17 at 23:06
• I like this answer. In the last part of (3) it could optionally be simplified to "is always some compound expression involving." I agree that "arithmetic" isn't helpful. What about "simple"? // I would not use "X" for the function since usually X is an independent variable; I would not use "i" since "i" is usually an integer. – aparente001 Feb 25 '17 at 0:24
• Your pie example does, indeed, express the sentence structure exactly as intended. For what it's worth, the actual sentence is on the subject of measures of information content and doesn't use any variable notation; I was just trying to abstract to a more general form. "Compounded" opens up several avenues. Synonyms like "composite" or even "joint" might also generate the inferences I'm looking for. Concerned that it not appear as if I'm naming a specific type of function, flipping it around as "functional compound" or similar, or else using "expression" is promising. Thanks all. – MDHunter Feb 25 '17 at 15:25

I would propose a supersizing function. With a more mathematical background, a majorizing function could also fit your needs but I did not get the precise objects behind your A or B.