How was the Battle of Britain a failure for Hitler?

Britain’s Royal Air Force destroyed the German air force.
The many months of bombing did not persuade the British to surrender.
The ground invasion by Nazi soldiers could not break Britain’s will to fight.
The Nazi navy lost a large number of ships and soldiers to the British.

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Answer:

By the end of October 1940, Hitler called off his planned invasion of Britain and the Battle of Britain ended. Both sides suffered enormous loss of life and aircraft. Still, Britain weakened the Luftwaffe and prevented Germany from achieving air superiority. It was the first major defeat of the war for Hitler.

It suffered from constant supply problems, largely as a result of underachievement in aircraft production. Germany's failure to defeat the RAF and secure control of the skies over southern England made invasion all but impossible.

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