◀ ▲ ▶Branches / Set-theory / Proof

Proof

(related to Corollary: Irrational Numbers are Uncountable)

• The set of real numbers $\mathbb R$ is uncountable, which was proven here.
• The set of rationals numbers $\mathbb Q$ is countable, which was proven here.
• Since the set of irrational numbers is defined as the set difference $\mathbb R\setminus\mathbb Q$, they are uncountable.
  ∎

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

1. Ebbinghaus, H.-D.: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition