Andries Brouwer <aebr@xxxxxxxxxx> writes:
David, did you read this line:These lemma are absolutely true.entropy(x) >= entropy(x xor y)Is this trolling? Are you serious?
entropy(y) >= entropy(x xor y)
Let us do it. Let z be an abbreviation for x xor y.Try to put z = x xor y and apply your insight to the strings x and z.
The lemma that you believe in, applied to x and z, says
entropy(x) >= entropy(x xor z)
entropy(z) >= entropy(x xor z)
But x xor z equals y, so you believe for arbitrary strings x and y that
entropy(x) >= entropy(y)
entropy(x xor y) >= entropy(y).
This "lemma", formulated in this generality, is just plain nonsense.
Not quite non-sense, but it would mean that for any strings x and y,
entropy(x) == entropy(y),
which seems incorrect.