hi,(adsbygoogle = window.adsbygoogle || []).push({});

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,

CC

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Uncountable domain

**Physics Forums | Science Articles, Homework Help, Discussion**