 As in his intermediate position, the later Wittgenstein claims that ‘\(\aleph_0\)’ and “infinite series” get their mathematical uses from the use of ‘infinity’ in ordinary language (RFM II, §60). Although, in ordinary language, we often use ‘infinite’ and “infinitely many” as answers to the question “how many?”, and though we associate infinity with the enormously large, the principal use we make of ‘infinite’ and ‘infinity’ is to speak of the unlimited (RFM V, §14) and unlimited techniques (RFM II, §45; PI §218). This fact is brought out by the fact “that the technique of learning \(\aleph_0\) numerals is different from the technique of learning 100,000 numerals” (LFM 31). When we say, e.g., that “there are an infinite number of even numbers” we mean that we have a mathematical technique or rule for generating even numbers which is limitless, which is markedly different from a limited technique or rule for generating a finite number of numbers, such as 1–100,000,000. “We learn an endless technique”, says Wittgenstein (RFM V, §19), “but what is in question here is not some gigantic extension”.