How do you represent infinity in a JSON API?

I would include a field "limit", which only exists when there really is a limit:

when the user has 40 left:

{
    "yourdata":"",
    "limit": 40
}

when the user has unlimited access remove it, meaning there is no limit:

{
    "yourdata":""
}

Number 1e500 is parsed as Infinity

console.log(1e500); // Gives Infinity

Or

JSON.parse('{"number": 1e500}'); // Gives {number: Infinity}

My suggestion is use numbers for specific values and strings for theoretical values. I think it's clearest.

{
  "shoes": 89,
  "cars": "infinity",
  "myBankAccount": "negative-infinity"
}

However, that doesn't seem to be the popular choice. I've seen -1,null, and undefined (absence of the property) mean unlimited in many cases.

At VMware, we use -1 to specify that there are no limits (memory, CPU, VMs) and we have had problems with using null because BlazeDS converted null to 0, and 0 was a valid value.

• -1 for unlimited bandwidth (Java API) (unlimited bandwidth)
• Null for unlimited (max_devices, max_storage_days)
• Undefined for unlimited (excluded from query string)