MathDB

Associate to any point

(h,k)

in the integer net of the cartesian plane a real number

a_{h,k}

so that a_{h,k}=\frac{1}{4}\left( a_{h-1,k} +a_{h+1,k}+a_{h,k-1}+a_{h,k+1}\right) , \forall h,k\in\mathbb{Z} .
a) Prove that it´s possible that all the elements of the set

A:=\left\{ a_{h,k}\big| h,k\in\mathbb{Z}\right\}

are different. b) If so, show that the set

A

hasn´t any kind of boundary.

Problem Statement