Just in case it’s not clear from the above: there are uncountably many degrees of freedom to an arbitrary complex function on the real line, since you can specify its value at each point independently.
A continuous function, however, has only countably many degrees of freedom: it is uniquely determined by its values on the rational numbers (or any dense set).
Just in case it’s not clear from the above: there are uncountably many degrees of freedom to an arbitrary complex function on the real line, since you can specify its value at each point independently.
A continuous function, however, has only countably many degrees of freedom: it is uniquely determined by its values on the rational numbers (or any dense set).