Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!feeder.erje.net!us.feeder.erje.net!newsfeed.fsmpi.rwth-aachen.de!news.swapon.de!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: Gregory Ewing Newsgroups: comp.lang.python Subject: Re: Working with the set of real numbers Date: Sat, 15 Feb 2014 00:30:15 +1300 Lines: 16 Message-ID: References: <8e4c1ab1-e65d-483f-ad9d-6933ae2052c3@googlegroups.com> <52f59aeb$0$29972$c3e8da3$5496439d@news.astraweb.com> <7cc8f49d-a4c7-48c2-a0af-ac58c847d794@googlegroups.com> <71e578f8-0d23-4b8e-b9f2-b987bdc9c01d@googlegroups.com> <85r478bv99.fsf_-_@benfinney.id.au> <85ioskbtfm.fsf@benfinney.id.au> <85eh38bq5z.fsf@benfinney.id.au> <871tz7864a.fsf@elektro.pacujo.net> <87fvnm7q1n.fsf@elektro.pacujo.net> Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: individual.net FQXG6zxxhFtxQcQUJr/zdAe3AvoLd544GLgjL8tQEXBKInB5s2 Cancel-Lock: sha1:klXPiC0/5ICW/uop80Eh3UYso5U= User-Agent: Mozilla Thunderbird 1.0.5 (Macintosh/20050711) X-Accept-Language: en-us, en In-Reply-To: Xref: csiph.com comp.lang.python:66291 Devin Jeanpierre wrote: > There is no way to iterate over all the reals one at a time, no matter > how fast you execute instructions. If you could, it would be trivial > to show that the reals have the same cardinality as the positive > integers: correspond n with the whatever is returned by the nth call > to it.next. You're assuming that the calls to it.next are discrete events separated by some nonzero time interval. A decent transfinite processor would make a continuum of calls, and execute uncountably many of them in any finite period of time. -- Greg