Prove \(f : \mathbb{Z}^+ \longrightarrow \mathbb{Z}\) given by \(f(n) = (-1)^n \cdot n\) is injective.

Prove that \(f : [0, \infty) \longrightarrow \mathbb{R}\) defined by \(f(x) = x^2\) is injective.

Learn how to prove a function is injective, or alternatively, is not injective.

Prove \(f : \mathbb{Z}^+ \longrightarrow \mathbb{Z}\) given by \(f(n) = (-1)^n \cdot n\) is injective.

Prove that \(f : [0, \infty) \longrightarrow \mathbb{R}\) defined by \(f(x) = x^2\) is injective.