Similarly, here is your reminder than US Zip Codes aren't numbers, because many of us here in the Northeast have them start with a zero (or even two). So don't store them as integers, because Boston is 02108, not 2108.
In general, addition is only meaningful in linear systems, but differences can be meaningful in affine systems.
A better litmus test is whether you can subtract values. The difference between two times, or two dates, or two temperature readings is something that is meaningful and commonly used in everyday life. The difference between two ZIP codes is nonsensical.
Nitpicking, but that seems like a great case for them being numbers. You will never average credit cards or zip codes. Averaging times is meaningful too (e.g. the mean arrival time).
I think op meant "adding" as generally doing math on them. Each quantity will have its own natural operations.
I see what you mean though, subtraction seems like a good heuristic by virtue of difference being mostly (always?) meaningful.
Not completely, there's a rough east-to-west pattern: https://d33wubrfki0l68.cloudfront.net/979d9b9012d8bbb1e4f14b...
So the difference is extremely crude geographic distance.
/evil