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    Is X uncountable if there exists a B subset of uncountable with X-B uncountable?

    Hi everyone! I have the following problem Homework Statement X is countable set if and only if the sigma-field 2_{X} is generated by the sets of the form \left\{\omega\right\} with \omega\in X Homework Equations The Attempt at a Solution The easy part is X is countable...
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