Suppose the amount of weight John gains from a meal is a function of the number of calories he eats, and that John will gain X weight, such that X>A, if he consumes Y calories, such that Y>B, where A is some lesser amount of weight less than X, and B is some number of calories less than Y.
In other words, we don't specify the exact correspondence, just the fact that the more John eats, the more weight he gains.
I don't know how I'd notate that in a way that I could use in a logical statement. Is there a concise way I could notate it?
Thank you,
-Hal
Let $w(x,y)$ denote the weight of person $x$ after consuming $y$ calories.
Thus, $w(x,0)$ gives the current weight of $x$ (after eating no calories), while $w(x,y)$ gives the weight of $x$ after eating $y$ calories. Similarly, $w(x,y) - w(x,0)$ gives the weight gain after consuming $y$ calories.
Then the relation you describe is expressed : $$ \text{if } y_1 \gt y_2, \text{ then } w(x,y_1) \gt w(x,y_2)$$