(A bit that over-ran from Exposure…)
A bit of Maths
The reasons aren’t as complicated as they’re often made out to be - the reason it’s an ‘f’ and a slash is that it’s a division calculation. ‘f’ is the focal length of the lens, and the result of the sum would be the actual aperture diameter. The reason photographers deal in the ratio, or the division calculation, rather than just talking about the actual width of the hole, is down to exposure. For a given level of light, at a given shutter speed, f/8 will always give the same result. It doesn’t matter what focal length lens you use. It all works out much simpler if you just use the ratios instead.
Awkward numbers
The problem with using ratios is that the numbers do end up being a bit awkward. You don’t need to worry too much about what they actually are, and you get used to them, but one ‘stop’ less light than f/2.8 is f/2. One ‘stop’ down from that is f/1.4. They aren’t numbered in nice round numbers.