Every separable metric space has cardinality less than or equal to the cardinality of the continuum.
This was stated in my book in a series of questions using the post office metric on $\Bbb R^2$, but I can't think of a way to prove this.
2026-03-26 19:19:01.1774552741
Every separable metric space has cardinality less than or equal to the cardinality of the continuum.
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