Pseudo-irrationals like π' are 'homeless' numbers.

Although a pseudo-irrational such as \(\pi '\) (on either definition) is “as unambiguous as … \(\pi\) or \(\sqrt{2}\)” (PG 476), it is ‘homeless’ according to Wittgenstein because, instead of using “the idioms of arithmetic” (PR §186), it is dependent upon the particular ‘incidental’ notation of a particular system (i.e., in some particular base) (PR §188; PR §182; and PG 475). If we speak of various base-notational systems, we might say that \(\pi\) belongs to all systems, while \(\pi '\) belon