- #1
happyg1
- 308
- 0
hi,
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
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