Now note, the inverse of monotonically increasing is not monotonically decreasing, which demonstrates what the semantic problem is. The unambiguous terminology for "as $x$ increases, $y$ increases" is monotonically increasing, and, to affirm that this is not local, the term strictly monotonically increasing is used, the inverse of which is then monotonically non-increasing and not strictly monotonically decreasing. For it to be an inverse, it would have to be an inverse of some algebraic operation, and the reason for using it in this context is otherwise, namely that it is inverse hand-waving of "as $x$ increases, $y$ increases type," and hand-waving is also not a defined algebraic procedure. The OP's question is: Is it correct to refer to a negative correlation as an 'inverse correlation'? The answer is no, correlation is intransitive, that is, given a correlation one cannot invert the procedure. What operation is an inverse of what other operation depends on which algebraic procedure is being used, for example, subtraction is inverse addition, division is inverse multiplication, deconvolution is inverse convolution, a matrix inverse is the inverse of an invertible matrix, an inverse Laplace transform is the inverse of a Laplace transform, and so on. In general, to keep the word inverse from causing confusion, all that need be done is to say inverse _ <- what and fill in the blank. Although true for definite positive inverse proportionality, this has the disadvantage of not being unique, as a negative slope direct proportionality has that same property. The concept of inverse proportionality is often approached at the beginner level by hand-waving in this fashion in this equation as $x$ increases, $y$ decreases. Similarly, it would be rare to use the phrase directly proportional to the negative of something, as it is easier to grasp a negative slope, and rework a phrase to accommodate that. More exact phraseology would be directly proportional and inversely proportional. That is inexact language use, of the type often called hand waving, with the advantage of helping students uncomfortable with the concept of proportionality to grasp the essentials of proportionality without using the word. In physics, more so than other things, one has occasion to say directly related and inversely related when speaking of proportional relationships.
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