# 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 |
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**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. | ||

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+ | Observation: The set of real numbers is not countable. | ||

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+ | 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. | ||