 Since, on Wittgenstein’s terms, mathematics consists exclusively of extensions and intensions (i.e., ‘rules’ or ‘laws’), an irrational is only an extension insofar as it is a sign (i.e., a ‘numeral’, such as ‘\(\sqrt{2}\)’ or ‘\(\pi\)’). Given that there is no such thing as an infinite mathematical extension, it follows that an irrational number is not a unique infinite expansion, but rather a unique recursive rule or law (PR §181) that yields rational numbers (PR §186; PR §180).