It'd help if we always used the correct mathematical notation for aperture which is F/1:4 but we call it f4 or sometimes f/4
The trouble with using the word 'mathematical', Phil, is that it attracts the mathematicians. And we can be a pedantic lot.
Unfortunately F/1:4 is not correct. The slash indicates a ratio, and the colon indicates a ratio, but you don't need or want to use both of them together.
You could write f/4 which is interpreted as a quarter of the focal length. Personally I think that's the clearest. Unfortunately we tend to say it as f 4 without the slash, and of course slashes can't be used in filenames or URLs so we're pretty much forced to use f4 on computers. That's not so good.
Alternatively you could write 1:4 which is interpreted as a ratio; something is four times bigger than something else. Of course we all know it means the focal length is four times the aperture, but it's not explicit and therefore (to my mind) less satisfying.
Interestingly the manufacturers can't agree which is the best way to indicate aperture. Canon and Nikon both write 1:4 on the lens, but f/4 on the box the lens comes in. Sigma write 1:4 on the lens but f4 on the box. Tamron aren't consistent. Tokina are consistent and use f4 everywhere, so you might say they're consistently wrong. Sony and Zeiss seem to derive their nomenclature from a parallel universe: instead of 70-200mm f/4 they'd write 4/70-200. But they all agree that it's not f/1:4.