Why does a mountain climber need an oxygen supply at very high altitudes, even though the air still contains 21% oxygen?

The air does not contain 21% oxygen at high altitutes. The figure would be closer to 16% although oxygen levels decrease the higher you go up. This is because oxygen is dense so it resides at the bottom of the atmosphere. The climber needs to make up for the low amounts of oxygen so uses an oxygen supply.

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The higher you go up the less oxygen there is