# How to say that something rises with the fall of something else

I want to write in a math article that one parameter is going up when other is falling. These parameters are linked. What is a formal way of writing it? "Parameter A is rise with the fall of parameter B"?

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## migrated from english.stackexchange.comApr 6 '11 at 10:45

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Going from a hunch, I would suggest "inversely proportional." If you are writing this article for a school or class you can probably get a great answer from a local math teacher or professor.

Edit: Okay, I guess I should have known that there was a technical definition of "inversely proportional." Wikipedia has a quick description, as do the comments here.

For example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.

So, inversely proportional is one type of rising with the fall of something else. A more generic term will be more appropriate.

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No: inversely proportional in mathematics usually means precisely that the two parameters multiply to a constant (e.g., as x rises y goes down because y=2/x). – msh210 Apr 5 '11 at 19:02
@Billare Actually, it's not entirely clear: The OP's question doesn't specify the rate at which one rises and the other falls. @msh210 is correct in that inverse proportionality applies only to a constant rate. It is simpler (and possibly more accurate) to say while one increases, the other will decrease. – HaL Apr 5 '11 at 19:26
@PLL I neglected to see the word "precisely" in msh2010's answer, having just read it over. I had realized what you were saying before, but still thought it wrong to say "no" or "wrong"; inversely proportional could very well be the relationship the OP is seeking, though I agree it is not the most general term one could use. – Uticensis Apr 5 '11 at 19:31
@msh; @pll: I edited with a correction and a bit more information. Apologies for the mistake and confusion. – MrHen Apr 5 '11 at 19:35
@darqer: I personally prefer @HaL's answer. – MrHen Apr 5 '11 at 19:36

Since it's math, you can use increase and decrease:

Parameter A will increase as Parameter B decreases.

Using the conjunction as links the two parameters correlatively.

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+1 for increase/decrease – MrHen Apr 5 '11 at 19:37

Perhaps you are looking for "negative correlation"

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"decreases monotonically with" if you are being technical.

That means A always goes up as B goes down (there are no inflections) - but you aren't saying anything about the relationship.

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If the increasing parameter is a function of the decreasing one, then you just call it a decreasing function of it. (The reason for this name will be clear when you graph the increasing parameter relative to the decreasing one on a pair of axes.)

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A and B are 'Inversely Proportionate'
Or A is inversely proportionate to B

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@MrHen suggested this already; as comments/edits on his answer show, it’s not exactly correct as an answer to the question, although it might fit the OP’s specific circumstances. – Peter LeFanu Lumsdaine Apr 5 '11 at 22:55

As one more possibility: "varies inversely".

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