Can we even know based off the definition of "number" once all the numbers have been described? There's natural, then integer, then rational, then real, then complex, then quaternions etc. and also surreal numbers, and probably also other more obscure stuff. Is there a limit to the types of extensions that can be made? The definition I find on wikipedia doesn't seem very formal, it's like "this is a number" is just a casual observation about a mathematical object with no real strict meaning.