Lemma 25.13.3. Let $X$ be a scheme. Points of $X$ correspond bijectively to equivalence classes of morphisms from spectra of fields into $X$. Moreover, each equivalence class contains a (unique up to unique isomorphism) smallest element $\mathop{\mathrm{Spec}}(\kappa (x)) \to X$.

**Proof.**
Follows from the discussion above.
$\square$

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