Inverse proportionality in set theory

[bahen]

Hi all,

I am wondering whether it is possible to describe inverse proportionality in set-theoretic notation. Specifically, I would like to describe the relation where increases in set A imply decreases in set B. There is a further complication which I can explain shortly about a subset of B, but I was hoping that this might be enough to get the ball rolling.

With thanks,
bahen

 

[Ishuda]

Hi all, I am wondering whether it is possible to describe inverse proportionality in set-theoretic notation. Specifically, I would like to describe the relation where increases in set A imply decreases in set B. There is a further complication which I can explain shortly about a subset of B, but I was hoping that this might be enough to get the ball rolling. With thanks, bahen

I'm not quite sure what you mean so I'll ramble a bit. Let f be a map (function) from set A to set B such that, if x belongs to A then f(x) belongs to B. For example consider the ordered set A = {1, 2, 3, 4} and the map f defined by f(x) = 0.5 x. Then B is the ordered set given by B = {0.5, 1, 1.5, 2} Of course this could also be other functions such as 'the volume of object f(x) is the inverse of the volume of object x'. Is this the sort of thing you mean?