Path: ...!Xl.tags.giganews.com!local-3.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 23 Nov 2024 21:52:48 +0000 Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (clock hypothesis) Newsgroups: sci.math References: <094dadad718eaa3827ad225d54aaa45b880dd821@i2pn2.org> <3399a95e386bc5864f1cfcfc9f91f48366e0fed2@i2pn2.org> <0d551828411c0588000796fa107a16b1e23a866c@i2pn2.org> <74bdc0f14fd0f2c6bfd9ac511a37f66b41948ac4@i2pn2.org> From: Ross Finlayson Date: Sat, 23 Nov 2024 13:52:48 -0800 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: Lines: 152 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-GgWrN7yHNE/HeBoUtPiW+x4oTPtpIvEfSuxWMRUCcBnViquMVfeQlLf57+1zSaz5aoBH6naEuSpDjdK!K7JlzV3EF2O5cyRb/N/Q0nDn7JglWptcV7rmCbpEfp/L0ttFhc+YmJbvwIdqs+Nf1XJ/gGCz0W6h X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 8408 On 11/23/2024 11:37 AM, Ross Finlayson wrote: > On 11/22/2024 05:09 PM, Ross Finlayson wrote: >> On 11/22/2024 01:08 PM, Chris M. Thomasson wrote: >>> On 11/22/2024 12:47 PM, Ross Finlayson wrote: >>>> On 11/22/2024 12:37 PM, Chris M. Thomasson wrote: >>>>> On 11/22/2024 6:51 AM, WM wrote: >>>>>> On 22.11.2024 13:32, joes wrote: >>>>>> > Am Fri, 22 Nov 2024 13:00:52 +0100 schrieb WM: >>>>>> >>>>>> >>>>>>>> The number of ℕ \ {1} is 1 less than ℕ. >>>>>> >>>>>>> And what, pray tell, is Aleph_0 - 1 ? >>>>>> >>>>>> It is "infinitely many" like Aleph_0. >>>>>> >>> Thanks for agreeing with |N| = |N\{0}|. >>>>>> >> Of course. ℵo means nothing but infinitely many. >>>>>> > Good. Then we can consider those sets to have the same number. >>>>>> > >>>>>> That is the big mistake. It makes you think that the sets of naturals >>>>>> and of prime numbers could cover each other. >>>>> >>>>> prime numbers are a sub set of the naturals. They are both infinite. >>>> >>>> Finite, though large, "sets", as though all the relations >>>> among them besides just "the set of", make it so in the >>>> asymptotics, that it's possible to work up when the >>>> density of primes, which is kind of known and on the >>>> order of log n, vis-a-vis pi^2/6 and co-primes, have >>>> it so that in some "practically" or "effectively" >>>> "un-bounded", if that's a short-hand interchangeable >>>> with "infinite", have only finitely many primes. >>>> >>>> Maybe one at infinity, .... >>> [...] >>> >>> How can there be one prime at infinity? That's like saying there is a >>> natural number at infinity. There is no largest natural just that there >>> is no largest prime. So, if you artificially say this prime is at >>> infinity you just went into finite mode! >>> >> >> Actually, some arrive at that if there are infinitely-many, >> then there is at least one infinitely-grand, in the same >> structure, of the same type. Called variously compactification, >> or fixed-point, it can be arrived at via plain comprehension >> the extra-ordinary, according to definitions of direct sum and >> product of copies of infinite sets, and in geometry it's >> usually called point-at-infinity, and lots of reasons. >> >> Then, "finite mode" as you put it, is as mentioned about >> variously "very, very large", yet only showing one side >> or the other what's "finite" or "infinite", meaning merely >> according to a definition of finite like I have, what happens >> in ordering theory, for example, these objects of the elements >> of discourse, il discorso. >> >> So, then that makes for a reading of somebody like AP, >> who has sorts of problems being stuck in finite mode, >> half-way, makes for a generous reading, because as is >> often put here, various under-informed reasonings about >> infinity, result incorrect conclusions. >> >> So, here's a generous reading, of your intuition, >> I've tried plentiful times to give something like WM >> reasons to say truthful things about things it's declared >> to declare, yet, it seems incorrigeable and even along >> the lines of a purposeful "soft-ball straw-man" of the >> easily mechanized sock-puppet toy of the sort launched >> by some childish, churlish chucklers, laughing at our >> expense (and dismay). >> >> Yet, while it's so wrong, then it's still necessary to >> shelter its bait-and-switch part of the proposition >> the bait, that must be upheld from getting trampled >> in the shuffle. >> >> > > > It's kind of like, meters/second and seconds/meter. > So, 0 meters/second is infinity seconds/meter, yet, > the idea is that in one dimension, for example, there's > a line with some arbitrary origin marked 0, and displacements > about that. Then, consider displacements as integers, > or displacements as rationals, or, displacements as > real numbers. So, given that position is an abitrary > function of time and to get there motion is an arbitrary > function of time and to get there acceleration is an > arbitrary function of time, each of the higher orders > of acceleration is an arbitrary function of time, and > any change at all affects a nominally non-zero, yet > vanishing, value each of the higher-order derivatives > of displacement (from the origin) with respect to time. > > So, 1 m/s = 1 s/m, with 0 m/s = infinity s/m, > and correspondingly infinity m/s = 0 s/m, though > it's usual the "rest" seems more likely than > "infinite velocity". > > An object at rest, then, is it, 0 m/s? As long as > it rests there, it is. Then, is it infinity s/m? > Potentially, ..., for as long as you count it's > 1, then 2, then 3, ..., infinity seconds / meter. > > While though its velocity is zero, the seconds > per meter is no less than infinity. > > So, if infinity is so bad, what about an origin? > > Then, there's an idea that x = y = z = ... the > identity line in all dimensions, is also an origin. > > Is there instantaneous anything at all? > > > Related-rates are simple enough, and of course > there is finite-element analysis and most people > know f = ma though it's really f(t) = ma(t), > how does anything ever change at all? > > > The regular singular points of the hypergeometric: > are: zero, one, and infinity, in mathematics. > > So, infinity seconds per meter, is it zero meters per second? Maybe not, then there's that t seconds per meter, grows, at a rate t, for time t, from zero, for as long as velocity equals zero meters per second. Then, thusly, it's again the _same_ thing, a constant velocity growing itself, while, as with respect to what's at rest, its origin and with all its infinitely-many higher orders of derivatives of displacement, or here velocity, with respect to time. It's a "moving quantity". So, then what this arrives at is a sort "clock hypothesis", that re-introduces t into all the otherwise instantaneous "quantities", "moving quantities". There's not finitely-many of those, so once again "infinity is _in_ (the numbers)". If you needed another reason why infinity is in, the numbers, here's a reason that you don't need another reason - it never left.