 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 \(\pi '\) belongs only to one, which shows that \(\pi '\) is not a genuine irrational because “there can’t be irrational numbers of different types” (PR §180). Furthermore, pseudo-irrationals do not measure because they are homeless, artificial constructions parasitic upon numbers which have a natural place in a calculus that can be used to measure. We simply do not need these aberrations, because they are not sufficiently comparable to rationals and genuine irrationals. They are not irrational numbers according to Wittgenstein’s criteria, which define, Wittgenstein interestingly asserts, “precisely what has been meant or looked for under the name ‘irrational number’” (PR §191).