Usually. A coin in Proof condition is almost always more valuable than the same coin in Uncirculated condition, but exceptions do exist.
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are diamonds more valuable than emeralds
Yes, by weight, diamonds are more valuable than gold.
All proof silver dollars are silver dollars, but not all silver dollars are proofs. That's because proof coins are specially struck for collectors, while (at least up till 1935 in the US) regular silver dollars were struck for use in ordinary commerce. Please see the Related Question for more details.
YES
No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more.