http://en.wikipedia.org/wiki/Measure_(mathematics) http://en.wikipedia.org/wiki/Measure_(mathematics) A measure is a function on the subsets of a space which y

http://en.wikipedia.org/wiki/Measure_(mathematics) http://en.wikipedia.org/wiki/Measure_(mathematics) A measure is a function on the subsets of a space which yields a non-negative real number. For example, a measure of the triangle with vertices (0,0), (2,0), and (6,0), is 6, the area of that triangle. Measure satisfies certain nice properties, such as if A is a subset of B, then the measure of A is no more than the measure of B. So, I guess if you can define a reasonable measure on the spaces X and Y, you can measure collections of X and collections of Y, and use the real numbers to determine which is "more". But this doesn't strike me as useful in any way other than the fun of abstract mathematics. :-)