Recent content by zelmac

Homework Statement Check whether the sequence a_{1}=\alpha ,\alpha > 0, a_{n+1}=6*\frac{a_{n}+1}{a_{n}+7} converges and find its limit if it does, depending on α. Homework Equations The Attempt at a Solution I showed boundedness([0,6]) and found that in the case of convergence...

I'm wondering whether my solution to this problem is correct, since the answer in the answer sheet says that this is provable, and I think I found a counterexample... Any help is appreciated :) Homework Statement Prove or disprove: ##f:D->K##, where ##D,K != empty##, is a bijection iff there...

You concluded: \exists{x}(P(x)\wedge{Q(x)}) and I'm wondering how do you get to: \exists{x}(P(x)\Rightarrow{Q(x)})

\exists{x}(P(x)\Rightarrow{Q(x)})\equiv{\forall{x}P(x)\Rightarrow{\exists{x}Q(x)}} I am able to derive this equivalence by using the standard equivalences of symbolic logic, but when I try to verify this semantically, with an example, I just can't see why these two expressions are equivalent...

Homework Statement Find the geometric image of the complex number z, if z, z^2, z^3 are the vertices of a right triangle. Homework Equations The Attempt at a Solution I tried expanding z^2, z^3, and than using both the pythagoras theorem, and vectors (in separate attempts), but...