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Minimal and Maximal Elements

  • Minimal and Maximal Elements #Card
    • For $A \subset X$: - $a_0 \in A$ is minimal if $A \ni a \le a_0 \implies a = a_0$. Denoted by $\text{Min } A$. - $a_0 \in A$ is maximal if $A \ni a \ge a_0 \implies a = a_0$. Denoted by $\text{Max } A$.

Back

Section titled “Back”

For $A \subset X$:

  • $a_0 \in A$ is minimal if $A \ni a \le a_0 \implies a = a_0$. Denoted by $\text{Min } A$.
  • $a_0 \in A$ is maximal if $A \ni a \ge a_0 \implies a = a_0$. Denoted by $\text{Max } A$.

Lean

Section titled “Lean”

Minimal / Maximal（Mathlib の述語）