Following my past few queries I've been wondering about stops and F values and stuff.
I know that 1 stop up or down is allowing twice or half the amount of light onto the sensor respectively and this can be done by changing the aperture or shutter speed.
With the shutter speed it's fairly easy to know what it means i.e. 1/1000 means the shutter is open for one one thousandth of a second. So using the same aperture and a speed of 1/500 is one stop higher.
With the aperture I know that F4 is one stop higher than F8 but what does the number equate to? Is it just an arbitrary number for that specific lens or if I use 1/500 shutter speed and F4 with one lens will it give the same results as using those settings with another lens? If so the number must mean something.
Also, my camera dial goes up and down in 1/3 stop intervals. Does this mean that if I change the aperture up 1/3 of a stop and the shutter speed down 1/3 of a stop will I be at the same exposure that I started with?
Lots and lots of questions

Not too important really but it's something I'd quite like to know.
Thanks