> (Side note: "identification number" really means "opaque string". IDs are not numbers. If adding or multiplying them together doesn't make sense, they're not numbers.)
Eeehhh I'm not sure if this necessarily true. A telephone number is definitely a number but addition doesn't make all too much sense on them.
If you want to specifically talk about objects that require addition and multiplication to be properly defined on them then you can always use Groups and Rings.
A phone number is definitely not a number - for example, it can often be written as starting with a +. Not only that, but one number can have multiple valid expressions (eg. a number with and without a country code). That's ignoring the different ways people like to format them (spaces, dashes, letters, etc.)
You could construct a telephone numbering system where the sum of two 'real' numbers could be dialed to start a three-way conference call. That would be.. amusing, to some subset of users.
A phone number is a number in a colloquial sense (a string of digits) but I would hate to use any computer system where phone numbers are stored or reasoned about as actual mathematical numbers.
Eeehhh I'm not sure if this necessarily true. A telephone number is definitely a number but addition doesn't make all too much sense on them.
If you want to specifically talk about objects that require addition and multiplication to be properly defined on them then you can always use Groups and Rings.