Nick_Hay2 comments on The Quantum Arena - Less Wrong

17 Post author: Eliezer_Yudkowsky 15 April 2008 07:00PM

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Comment author: Nick_Hay2 20 April 2008 01:57:45AM 0 points [-]

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).