$|\mathbb{N}| < |\mathbb{Z}|$

$|\mathbb{N}| = |\mathbb{Z}|$ (both countably infinite)

$|\mathbb{Q}| < |\mathbb{R}|$ ($\mathbb{R}$ is uncountable)

$|\mathbb{Q}| = |\mathbb{N}|$ (both countably infinite)