ThmDex – An index of mathematical definitions, results, and conjectures.

Bijection from the set of natural numbers to the set of integers

Formulation 0

Let $f : \mathbb{N} \to \mathbb{Z}$ be a D3639: Standard sequence such that

(i)	\begin{equation} f(n) : = (-1)^n \left\lfloor \frac{n + 1}{2} \right\rfloor \end{equation}

Then $f$ is a D468: Bijective map from $\mathbb{N}$ to $\mathbb{Z}$.