Uncountable set
A set is uncountable if it is not countable.
Definition 6.11 (Uncountability)
A set is uncountable if it is not countable.
Examples
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is uncountable, hence so are and every interval in .
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is uncountable.
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Consequently there are uncountably many transcendental numbers.
Showing uncountability
To show that a set is uncountable:
- use a diagonal argument, or
- inject an uncountable set into .
Related
Stated in
- Definition 6.11 (Uncountability)§6 Countability