# Thread: Countable Principle of Choice

1. ## Countable Principle of Choice

Prove, using the Countable Principle of Choice, that every countable subset of $\omega_1$ has an upper bound in $\omega_1$.

Notation: $\omega_1$ denotes the first uncountable ordinal.

2. Hi

Hint: With the countable principle of choice, a countable union of countable sets is also countable.