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Cardinality Comparison

  • Cardinality Comparison #Card
    • $\text{card } X \le \text{card } Y$ if there exists an injection from $X$ to $Y$ (or if $X \neq \emptyset$, a surjection from $Y$ to $X$). - Strict inequality $\text{card } X < \text{card } Y$ holds if there is no injection from $Y$ to $X$.

Back

Section titled “Back”

$\text{card } X \le \text{card } Y$ if there exists an injection from $X$ to $Y$ (or if $X \neq \emptyset$, a surjection from $Y$ to $X$).

  • Strict inequality $\text{card } X < \text{card } Y$ holds if there is no injection from $Y$ to $X$.

Lean

Section titled “Lean”

Cardinal の ≤ / Cardinal.le_def