Olin Lathrop wrote:
>> Since for every possible real number x there is a number f(x) which is
>> either zero or one, it seems to be that it would be continuous.
>
> No, that's not what continuous means.  Think of graphing the funtion.
> If you have to lift your pencil it's discontinuous.

Now that I read this again, I think I see the misconception.  Continuous
says something about the function's value, not it's domain.  Or to put it in
the context of this example, continuous means abrupt jumps in Y.  It is not
about all value so X being "filled in".


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