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"?
How to say that something rises with the fall of something else
7 Answers
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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0What about *inversely related*? – 2011-04-05
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.
Perhaps you are looking for "negative correlation"
"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.
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.)
A and B are 'Inversely Proportionate' Or A is inversely proportionate to B
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0@MrHen [suggested this already](http://english.stackexchange.com/questions/19607/how-to-say-that-something-rises-with-the-fall-of-something-else/19609#19609); 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. – 2011-04-05
As one more possibility: "varies inversely".