# 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

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."