Recent content by cris(c)

Hi guys, I need some help please! Consider the following expression: \left[1-\int_{x}^{1}F(\rho(\xi))f(\xi)d\xi\right]^{n-1} where F:[0,1]\rightarrow [0,1] is a continuously differentiable function with F'=f, x∈[0,1], and n>2. Suppose that \rho belongs to the set of continuous and...

A mistake in my previous post. Indeed, to prove ~Q implies ~P you have to show that for some e>0, x > y → x > y+ε, since negating Q means that there is at least one e>0 such that ~Q is true.

you can't negate saying that you need an epsilon greater than zero. The negation must be done looking for some nonnegative epsilon. Any will do it, in particular epsilon=y-x.

any one out there willing to help?

It should. The negation of x≤ y+ε  for every ε > 0 requires X>y+e for some e<0.

I guess you're right! P cannot imply both A and ~A...

negating a statement...need help urgently! Hi everyone: I am not sure about the following thing I did. Let J be a countable finite set, and f_{jk}^{0} and f_{jk}^{1} be two continuous functions defined on [0,1]. Consider the following statement: \forall lj\in J,\forall x\in[0,1],\: \...

Hi again, It appears that your answer is not completely correct or I am truly messed up. Negating (Q and Z) means that either (Q and not Z) or (Z and not Q). Hence, to actually show that P implies (Q and Z), don't we need to show that both of the above cases aren't possible true? I mean...

Suppose I know that [(P implies ~A) and (P implies B) and (P implies C)] is impossible. Does this means that the following statement is true: [(P implies A) and (P implies B) and (P implies C)]? Any help is greatly appreciated!

Think I got it. Thanks a lot!

This means that the proof is complete if I assume (say) case (i) to be true and arrive to a contradiction?

Homework Statement Suppose I want to prove the following statement by contradiction: P \longrightarrow (Q \land Z) Homework Equations If (Q \land Z) is false, then either: (i) Q is false and Z is true; (ii) Q is true and Z is false; (iii) Q and Z are false. The Attempt at a...

Thanks SammyS. I thought exactly the same as you. However, I still don't see why the chain rule would be invalidated in this case. I know that so long as y does not appear in the limits of integration the integral should not change with y, but why the chain rule doesn't appear to say the sameÉ

Homework Statement Consider three univariate distinct functions f_1(x),f_2(y),f_3(y). Let H be given by the following integral: H=\int_{0}^{f_1(x)} G(f2(\xi))G(f3(\xi))d\xi The Attempt at a Solution Then, computing dH/dy should give zero. However, I am not certain of this because...

Thanks a lot for your clarifying answer...this really helps a lot!