The "range" is merely established by convention. If your computer supports 100 distinct values then you could say those values represent the integers [0,100) or you could say they represent the even integers in [0,200). The range can be arbitrarily large, but the precision is fixed.
Arbitrary precision is the correct terminology. I can already represent any size integer I want on any computer. I could just declare that MAXINT represents Graham's number (for example). That doesn't mean that I can represent every integer between zero and Graham's number, though.
Yeah that good for MacOS and virtually every other piece of technology.