Your assumptions are mathematically impossible for the range of values you selected. Your biggest mistake was creating a function to abbreviate a simple ratio.

Let's examine just your case 3. Here are your assumptions.

(1) V(A, B) = A/B

(2) >V(A, B) = V(A, A) + V(A, B-A)

(3) >In case 3, A < B

(4) Where A, B are real, positive integers.

End assumptions. Therefore, starting with assumption (2), we have:

A/B = A/A + A/(B-A)

A/B = 1 + A/(B-A)

A(B-A)/B = B - A + A

(AB - A^2)/B = B

A² - AB + B² = 0

A² + B² = AB

From assumption (3), we know that B>A, and, therefore, B² > AB.

If B² is a bigger, real, positive integer than AB, then the sum of B² with another real, positive integer (A²⁾ must also be greater than AB. There are no values within your constraints that satisfy this equality.