How do you prove loss and gain?

Question

Why is gain equal to final value minus initial value, loss equal to initial value minus final value? How do you prove them mathematically?

Answer 1

This is because gain shows the amount by which the final value exceeds the initial value, whereas loss shows the amount by which the final value is less than the initial value. When we say 'amount' we mean the absolute value of the difference.
The actual difference we take is $V_f - V_i$ ($V_i=$ initial value, $V_f=$ final value), so when we say 'loss', we actually say that we 'gained' the negative of the amount lost. So, the amount lost is $|V_f - V_i|$ ($V_f < V_i$) = $V_i - V_f$, while the amount gained is $V_f - V_i$ ($V_f > V_i$).

Saying the truth , we don't need to prove anything. The definitions themselves imply what we need to know.

Please do tell me if any definition sounds ambiguous.