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Here's the most problematic language. more light doesn't equal higher f:stops, but More light means you need the higher numbered f:stops since they let in Less light.
So it may be more clear to say, that the larger openings use the smaller numbers and the Larger the opening, the more light is let in for any given shutter speed.
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But they are not higher-numbered f-stops. f/16 is a smaller number than f/11, and f/11 is a smaller number than f/8, and so on. Larger openings use larger numbers.
Granted, some use "f8", "f11", and "f16", but in a mathematical sense they aren't the correct expressions for the diameter of the aperture.