Let $(X, \mathcal{B}_X)$ and $(Y, \mathcal{B}_Y)$ be standard Borel spaces. If $|X| = |Y|$ (as sets), then $(X, \mathcal{B}_X)$ and $(Y, \mathcal{B}_Y)$ are Borel isomorphic: there exists a bijection $f: X \to Y$ such that both $f$ and $f^{-1}$ are Borel measurable. In particular, every uncountable standard Borel space is Borel isomorphic to $(\mathbb{R}, \mathcal{B}(\mathbb{R}))$.