If $d$ is a fixed positive integer, let $\Lambda_N$ be a finite subset of $Z^d$, the lattice points of $\mathbb{R}^d$, with $\Lambda_N \uparrow Z^d$ and satisfying ...

Multiplying by an Expression That Can Be Zero: This is the most common culprit. If you multiply both sides of an equation by an expression that could potentially equal zero for some value of the ...