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the question I am working on is this:

If f:A-->B and the range of f is uncountable, prove that the domain of f is uncountable.

Intuitively this seems to be true. If the range is uncountable, then function has to map an uncountable number of elements from the domain to the range. I don't know how to make this a rigorous proof. Does the function have to be one to one? Can I say that the inverse exists? I know that this is an easy problem, but I am stuck. Please point me down the right path.

Thanks,

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