Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > alt.slack > #509253

Re: Mapping reals to integers

Cross-posted to 4 groups.

Show all headers | View raw

Ross Finlayson wrote:
> On 05/07/2026 08:26 AM, jojo wrote:
>> phoenix wrote:
>>> jojo wrote:
>>>> i wanted to say something about reals and integers.
>>>>
>>>> reals are probably not real in the universal sense that the universe
>>>> we inhabit is continuous along a real line.
>>>>
>>> Physicists continue to wonder whether there is a smallest unit of time
>>> that there cannot be smaller than but haven't had any success recently
>>> narrowing the problem down.
>>>
>>
>> speaking of time, have you heard that zeno guy and his paradox?
>>
>> does it prove that the universe is discrete and not continuous?
>>
> 
> Actually here it's established since at least about a decade
> that the iota-values the range of the equivalency function
> have least-upper-bound and sigma-algebras the measure 1.0,
> thusly having extent density completeness measure and
> thusly being a continuous domain, that there's only and
> exactly this one functions between N and [ 0,1 ] that's
> a bijective function (being one-to-one and onto, both
> an injection and a surjection, a function), this the
> "natural/unit equivalency function" or "N/U EF" or "EF",
> then having also its reverse image (1 - EF = REF,
> "reverse equivalency function"), so that the continuous
> and discrete have a relation that's a _countable_ continuous
> domain the continuous, while though the function so defining
> it is a _non-Cartesian_ function, so that besides falling out
> of the arguments otherwise for un-countability as un-contradicted,
> that also as non-Cartesian it stays out of the way of the
> Cantor-Schroeder-Bernstein and can't be cancelled away algebraically.
> 
> So, these are "line-reals" not "field-reals" the usual standard
> complete-ordered-field after fractions and rationals the
> ordered field the "completion" of those, also it makes ground for there
> existing instead of being "axiomatized" the completion of the complete
> ordered field.
> 
> 
> There's the other account of a countable continuous domain,
> the "signal-reals", about that there's a model of rationals
> that since a continuous domain exists, that this sort of
> f: Q <-> S \ Q is a bijection between Q and a countable
> continuous domain, the signal-reals.
> 
> 
> That the universe is continuous is always formally non-falsifiable,
> so it's un-scientific to say so, though it can be scientific to
> say that a discrete approximation approaches particular accuracies.
> 
> Then "running constants" in real theory paint-cans or
> throws water on otherwise those claiming "grainy universe".
> 
> 
What is your reason for focusing on [0,1]?

 From what you've told me, the integers map to any set [-M,M] for any M 
no matter how large.

Unfortunately, this does not mean that M can be positive infinity, 
however, which is where it would break down and no longer work.

-- 
War in the east
War in the west
War up north
War down south
War War

Back to alt.slack | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

Mapping reals to integers phoenix <j63840576@gmail.com> - 2026-05-04 07:58 -0600
  Re: Mapping reals to integers "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-05-04 15:18 -0700
    Re: Mapping reals to integers "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-05-04 15:24 -0700
      Re: Mapping reals to integers Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-04 16:51 -0700
        Re: Mapping reals to integers Brennus <brennus@allia.org> - 2026-05-05 19:47 +0000
          Re: Mapping reals to integers % <pursent100@gmail.com> - 2026-05-05 13:48 -0700
            Re: Mapping reals to integers jojo <f00@0f0.00f> - 2026-05-07 14:53 +0000
              Re: Mapping reals to integers phoenix <j63840576@gmail.com> - 2026-05-07 09:02 -0600
                Re: Mapping reals to integers jojo <f00@0f0.00f> - 2026-05-07 15:26 +0000
                Re: Mapping reals to integers Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-09 11:12 -0700
                Re: Mapping reals to integers phoenix <j63840576@gmail.com> - 2026-05-09 12:25 -0600
                Re: Mapping reals to integers Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-09 11:35 -0700
                Re: Mapping reals to integers phoenix <j63840576@gmail.com> - 2026-05-09 12:46 -0600
                Re: Mapping reals to integers Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-09 11:51 -0700
                Re: Mapping reals to integers % <pursent100@gmail.com> - 2026-05-09 11:45 -0700
                Re: Mapping reals to integers cRudey Canoza <rc@hendry.con> - 2026-05-09 21:45 +0100
                Re: Mapping reals to integers jojo <f00@0f0.00f> - 2026-05-09 20:55 +0000

csiph-web