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The problem with your assumption is that you're assuming there are a finite number of states. There might be an uncountably infinite number of states, for insta
by wizzwizz4 5y ago
The problem with your assumption is that you're assuming there are a finite number of states. There might be an uncountably infinite number of states, for instance if the states were the reals between 0 and 1.
- chriswarbo 5y agoWhich assumption are you referring to? If it's about the states in a finite region, note that I specifically limited this to distinguishable states. Whether or not a finite region can have an infinite number of states (countable or otherwise) is irrelevant; we can only distinguish finitely many in finite time. Two states being indistinguishable means they'll give rise to the same output behaviour (e.g. from a mathematician in a room, carrying out some procedure).