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Uncountability

  • Uncountability #Card
    • A set $X$ is uncountable if it is not the image of $\mathbb{N}$ ($\text{card } X > \aleph_0$). - The set of real numbers $\mathbb{R}$ is uncountable (Proposition I.5.7). Its cardinality is denoted by $\mathfrak{c}$ (continuum).

Back

Section titled “Back”

A set $X$ is uncountable if it is not the image of $\mathbb{N}$ ($\text{card } X > \aleph_0$).

  • The set of real numbers $\mathbb{R}$ is uncountable (Proposition I.5.7). Its cardinality is denoted by $\mathfrak{c}$ (continuum).

Lean

Section titled “Lean”

¬ Countable X / カントール thm_I_5_8_cantor