aashish.v said:1. Prove that: F(x1,x2,...xn)<=min Fi(xi)
Where F is a DF on (x1...xn)
I know that this is very intuitive. But I am not able to find proper mathematical argument for that.
This notation means that the value of the function F, when evaluated at values x1, x2, ... xn, is less than or equal to the minimum value of the individual functions Fi evaluated at their respective values xi.
To prove this statement, you would need to show that for any values x1, x2, ... xn, the value of F(x1,x2, xn) is always less than or equal to the minimum value of Fi(xi). This can be done through mathematical manipulation and logical reasoning.
Yes, this statement can be proven for any functions F and Fi, as long as they are well-defined and satisfy the necessary conditions for mathematical proofs.
This statement is applicable in any situation where a function F is compared to a set of other functions Fi, and it is desired to show that F is always less than or equal to the minimum value of Fi.
This statement is important in scientific research because it allows us to make conclusions about the behavior of a function F based on the behavior of a set of other functions Fi. This can help us understand and analyze complex systems and make predictions about their behavior.