I just read that there are an uncountable number of countable ordinals.
How the hell is that possible?
The set(!) of countable ordinals is itself an ordinal (well-ordered and transitive). If this ordinal were countable, it would be an element of itself.
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The set(!) of countable ordinals is itself an ordinal (well-ordered and transitive). If this ordinal were countable, it would be an element of itself.