# Differences

This shows you the differences between two versions of the page.

 sav08:countable_set [2008/03/10 16:27]vkuncak created sav08:countable_set [2008/03/10 16:29] (current)vkuncak 2008/03/10 16:29 vkuncak 2008/03/10 16:27 vkuncak created 2008/03/10 16:29 vkuncak 2008/03/10 16:27 vkuncak created Line 13: Line 13: **Theorem:​** if $A, B$ are countable then $A \cup B$ and $A \times B$ are countable, but $2^A$ is not countable. **Theorem:​** if $A, B$ are countable then $A \cup B$ and $A \times B$ are countable, but $2^A$ is not countable. + Observation:​ The set of all strings over some finite alphabet is countable.  ​ + + Observation:​ The set of real numbers is not countable. + + Observation:​ If the set $A$ is infinite and the set $B$ has at least two elements, then set of all functions $f : A \to B$ is not countable.