 An infinite sequence, for example, is not a gigantic extension because it is not an extension, and ‘\(\aleph_0\)’ is not a cardinal number, for “how is this picture connected with the calculus”, given that “its connexion is not that of the picture | | | | with 4” (i.e., given that ‘\(\aleph_0\)’ is not connected to a (finite) extension)? This shows, says Wittgenstein (RFM II, §58), that we ought to avoid the word ‘infinite’ in mathematics wherever it seems to give a meaning to the calculus, rather than acquiring its meaning from the calculus and its use in the calculus. Once we see that the calculus contains nothing infinite, we should not be ‘disappointed’ (RFM II, §60), but simply note (RFM II, §59) that it is not “really necessary… to conjure up the picture of the infinite (of the enormously big)”.