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NNTP-Posting-Date: Mon, 30 Dec 2024 02:12:46 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (replete large numbers)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 29 Dec 2024 18:12:59 -0800
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On 09/07/2024 08:27 AM, Ross Finlayson wrote:
> On 09/07/2024 03:30 AM, FromTheRafters wrote:
>> Ross Finlayson presented the following explanation :
>>> On 09/06/2024 03:31 PM, FromTheRafters wrote:
>>>> WM has brought this to us :
>>>>> On 06.09.2024 20:17, FromTheRafters wrote:
>>>>>> WM submitted this idea :
>>>>>
>>>>>>>> What the Hell could mean "to increase at an x" ?
>>>>>>>
>>>>>>> Example: The function f(x) = [x] increases at every x ∈ ℕ by 1.
>>>>>>
>>>>>> Make up your mind, is x real or natural.
>>>>>
>>>>> ℕ c ℝ.
>>>>
>>>> So what? There is no natural number of unit fractions less than any
>>>> positive real or natural number. You said x was real in another post
>>>> and
>>>> here you claim it is natural. The output of your function is a constant
>>>> Aleph_zero not a continuum.
>>>
>>> Some number theorists have that there's a point at infinity
>>> and it's natural that way.
>>>
>>> The first "counterexample in topology" in "Counterexamples in Topology"
>>> is that there's a smallest non-zero iota-value.
>>>
>>> When there are at least three models of real numbers,
>>>
>>> line-reals
>>> field-reals
>>> signal-reals
>>>
>>> after an Integer Continuum a la Scotists and before a
>>> Long-Line Continuum a la duBois-Reymond, and there are
>>> at least three law(s) of large numbers, and at least
>>> three models of Cantor Space the square, sparse, and signal,
>>> in a world where Vitali and Hausdorff already proved the
>>> existence of doubling-spaces and doubling-measures before
>>> there were Banach and Tarski, then it gets into that
>>> "natural" is of a more replete surrounds than counting numbers.
>>
>> However, if one desires to add two plus four, it is not necessary to use
>> complex numbers as your domain and codomain just because the naturals
>> are contained in the complex number system. This, a form of the K.I.S.S.
>> priciple. He wants to use the reals so he can pretend that there is a
>> smooth sweep across all values in the interval. In reality each of his
>> values is jumped to and there are Aleph_zero of them as each is defined
>> as next (successor function) to the previous.
>
> "Keep it simple, stupid", is reasonable but at some point it's
> too dumb, even though everyone always hauls out the old "according
> to Einstein, things should be as simple as possible, no, even
> simpler", at some point in time that's too dumb.
>
> As a continuous domain or the linear continuum, there are only
> and everywhere and all real numbers between zero and one,
> and there being three models of them indicates _variously_
> their construction and access.
>
> Paucity and a natural elegance in being trim is appreciated,
> this is the all of mathematics' continuous domains and the
> linear continuum in all its roles, a bit of book-keeping
> has that at some point it's simpler to have all three and
> keep track of their differences than one that gets dumb.
>
>