You can breathe well above 11,000 feet; I don't think breathing is dangerously impaired until 18-20,000 feet. People around here climb Mt. Rainier without oxygen, and it's 14,000 feet.
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YOU ARE CORRECT
Partially correct... As was explained later. Acclimation is the key. A gradual loss of Oxygen is tolerable to the body. A sudden decrease of Oxygen will cause you to pass out. Hence the struggle with atheletes competing in Boulder, CO when being used to competing in lower altitudes.