I've read that it is unsatisfactory to consider infinitely many basis vectors to span an infinite dimensional space. For example, for the infinite dimensional Hilbert space, {e1,e2,e3.......} we could use this to make an arbitrary infinite tuple (a,b,c,...). If this is looked down upon, then why are Supernatural Numbers, which are the product of infinitely many primes, considered ontologically valid ?(adsbygoogle = window.adsbygoogle || []).push({});

Surely if we do a transformation, we could express those supernatural numbers as vectors, since its just converting multiplication to vector addition.

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# A Infinite Basis and Supernatural Numbers

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