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I'm trying to convince myself that the conditional entropy of a function of random variable X given X is 0.

H(g(X)|X)=0

The book I'm reading (Elements of Information Theory) says that since for any particular value of X, g(X) is fixed, thus the statement is true. But I don't understand why this makes the conditional entropy 0.

Obviously I don't understand conceptually what conditional entropy really is...

Can anyone please provide some "gentle" insight into this?

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# Conditional Entropy, H(g(X)|X)

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