Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many ... (Sparse, Signal, Square Cantor "SPACE")
Date: Sun, 3 Nov 2024 21:11:20 -0800
Organization: A noiseless patient Spider
Lines: 120
Message-ID: <vg9l1p$q3ee$2@dont-email.me>
References: <vb4rde$22fb4$2@solani.org> <vfnpf2$ukv3$1@dont-email.me>
 <vfns3j$3r5kq$2@i2pn2.org> <vfoq1m$14lcd$4@dont-email.me>
 <vfp9q0$3tqss$3@i2pn2.org> <vfq750$1fqil$2@dont-email.me>
 <vfqfpk$3vms5$2@i2pn2.org> <vftjuj$26ql1$2@dont-email.me>
 <30dffbdf129483f7b61e3284d1e7bf2ad2e5ea16@i2pn2.org>
 <vg0f4f$2p50e$2@dont-email.me>
 <9ca97f4a24ae1e3041583265125cf860d2fada11@i2pn2.org>
 <vg2bfl$375p7$1@dont-email.me> <vg2c64$3799e$1@dont-email.me>
 <vg2eju$37aml$1@dont-email.me> <vg2hr4$388sl$1@dont-email.me>
 <vg31kv$3av1t$1@dont-email.me> <vg37a2$3c03d$1@dont-email.me>
 <vg3cd7$3cnhr$1@dont-email.me> <vg3il2$3dueg$1@dont-email.me>
 <vg4t58$3nd3l$2@dont-email.me> <vg5avi$3qjkj$1@dont-email.me>
 <ELqdndl4Qvrg9Lv6nZ2dnZfqnPoAAAAA@giganews.com>
 <vg61ls$3ukov$4@dont-email.me>
 <7KednW4Tm59PP7v6nZ2dnZfqn_ednZ2d@giganews.com> <vg6rd6$6v0d$2@dont-email.me>
 <WlqdnS76wYzHM7r6nZ2dnZfqn_udnZ2d@giganews.com> <vg8ut4$ik8k$6@dont-email.me>
 <V8ydnWsTtNiphbX6nZ2dnZfqn_udnZ2d@giganews.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 04 Nov 2024 06:11:22 +0100 (CET)
Injection-Info: dont-email.me; posting-host="a3560c29bf30eac6bd9d64bfc512bec5";
	logging-data="855502"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19S5p6s6sc5Ul8vNbxAFmQkFo4/gfnluiw="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:NULcNWGyjou71CfLOnWp54yRmnI=
Content-Language: en-US
In-Reply-To: <V8ydnWsTtNiphbX6nZ2dnZfqn_udnZ2d@giganews.com>
Bytes: 6432

On 11/3/2024 4:41 PM, Ross Finlayson wrote:
> On 11/03/2024 02:53 PM, Chris M. Thomasson wrote:
>> On 11/3/2024 9:09 AM, Ross Finlayson wrote:
>>> On 11/02/2024 08:41 PM, Chris M. Thomasson wrote:
>>>> On 11/2/2024 3:08 PM, Ross Finlayson wrote:
>>>>> On 11/02/2024 01:22 PM, Chris M. Thomasson wrote:
>>>>>> On 11/2/2024 11:03 AM, Ross Finlayson wrote:
>>>>>>> On 11/02/2024 06:54 AM, FromTheRafters wrote:
>>>>>>>> WM was thinking very hard :
>>>>>>>>> On 01.11.2024 22:53, FromTheRafters wrote:
>>>>>>>>>> WM explained on 11/1/2024 :
>>>>>>>>>>> On 01.11.2024 19:39, FromTheRafters wrote:
>>>>>>>>>>>> WM formulated the question :
>>>>>>>>>>>
>>>>>>>>>>>>>> Infinite subsets don't do that for you, even if you wish
>>>>>>>>>>>>>> really
>>>>>>>>>>>>>> hard.
>>>>>>>>>>>>>
>>>>>>>>>>>>> They cannot evade if they are invariable.
>>>>>>>>>>>>
>>>>>>>>>>>> Sets don't change.
>>>>>>>>>>>
>>>>>>>>>>> Therefore the elements do not depend on us and our knowledge.
>>>>>>>>>>> "If I
>>>>>>>>>>> find x, then I can find x + 1" is not relevant. "For every x
>>>>>>>>>>> (that I
>>>>>>>>>>> find) there is x + 1" is no relevant. All elements are there,
>>>>>>>>>>> independent of what we know or do. Therefore the first and the
>>>>>>>>>>> last
>>>>>>>>>>> are also there independent of us. If they weren't, their
>>>>>>>>>>> existence
>>>>>>>>>>> would depend on some circumstances and could change.
>>>>>>>>>>
>>>>>>>>>> Circumstances like "there is no last element"?
>>>>>>>>>
>>>>>>>>> That means, there is always another element. Potential infinity.
>>>>>>>>
>>>>>>>> Sets don't change. Forget about amplifying 'not finite' with 
>>>>>>>> such as
>>>>>>>> 'actual' and potential' -- infinite simply means not finite and
>>>>>>>> 'actual/potential' is a distinction without a difference. A useless
>>>>>>>> concept outside of math philosophy.
>>>>>>>>
>>>>>>>>>> the set of denominators have no largest element to 'start' with.
>>>>>>>>>
>>>>>>>>> If all unit fractions are existing, then a smallest unit
>>>>>>>>> fraction is
>>>>>>>>> existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions
>>>>>>>>> must
>>>>>>>>> be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of
>>>>>>>>> uncountably many points must be between 0 and x₀. That cannot
>>>>>>>>> happen
>>>>>>>>> at x₀ = 0.
>>>>>>>>>
>>>>>>>>> Is that too hard to understand?
>>>>>>>>
>>>>>>>> Apparently, for you.
>>>>>>>
>>>>>>> Au contraire, there are multiple law(s) of large numbers,
>>>>>>
>>>>>> What about this sucker (42^999429994299942) * 2 ?
>>>>>>
>>>>>> Oh, don't forget about ((42^999429994299942) * 2) + 1   damn it!
>>>>>>
>>>>>>
>>>>>>
>>>>>>> and in mathematics like emergence after convergence,
>>>>>>> the potential / practical / effective / actual distinction,
>>>>>>> of "infinity", is a thing.
>>>>>>>
>>>>>>> You know who discovered mathematics? Philosophers.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>> Well, I frame it about Cantor space, because, there are
>>>>> some facts deducible from the asymptotic density of zero's
>>>>> and one's, in the rows and columns Cantor space, even if
>>>>> there are infinitely or trans-finitely many.
>>>> [...]
>>>>
>>>> Cantor Pairing is fun. Mapping to and fro. Nothing is lost. WM 
>>>> disagrees
>>>> here, but shit happens.
>>>>
>>>>
>>>>>
>>>>
>>>
>>> Here's a way to think about it.
>> [...]
>>
>> Cantor pairing works, and nothing is lost. That's that.
>>
> 
> Numbering and counting ("pairing") are two different things,
> much like order theory and set theory are two different things,
> Cartesian and non-Cartesian functions are two different things,
> ordinals and cardinals are two different things,
> and non-Cartesian orderings in numberings are not pairings,
> and won't be lost.

Well, we can turn two naturals into a single and unique natural, then 
convert that back to the two original naturals. They were always there 
to begin with because the naturals have no end... ;^)


> 
> Don't get me wrong, I've lots experience with pairing, ...,
> yet it works out that counting is not numbering,
> and that counting does not suffice all cases of numbering.
> 
> 
> Or, "Eudoxus/Cauchy/Dedekind is not sufficient",
> though it's great for what it is,
> it's not sufficient for a theory of everything,
> and it's _not_ complete there.
> 
>