Path: csiph.com!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Jim Burns <james.g.burns@att.net>
Newsgroups: sci.math
Subject: =?UTF-8?B?UmU6IGJlY2F1c2UgZ+KkqChn4oG7wrkoeCkpID0gZyh5KSBbMS8yXSBS?= =?UTF-8?Q?e=3A_how?=
Date: Mon, 22 Apr 2024 15:36:14 -0400
Organization: A noiseless patient Spider
Lines: 48
Message-ID: <fd080bee-e8af-4984-b463-288a67d8f9fc@att.net>
References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <922aae5f-6e7f-477d-b4f7-ce81f205e50f@att.net> <i2V5gF-N-1t5AOZtY8EToeouuh0@jntp> <8edceb74-d356-4e99-81d5-76eeb05df4a8@att.net> <I_pgw0s99BTbmlSbhNszXL_WH0I@jntp> <92c0ddf5-48e7-4605-bff1-ffe03faa9dd4@att.net> <jfuiGHn7MmP2gzZbv-rgY3zFfIU@jntp> <f4fbf78e-09e4-4042-9005-cbe5ca4f0623@att.net> <SMXuukb36RM2p0GDxOFCfgENLmE@jntp> <2eae07d8-365b-4dc4-8011-5858dc4a6c4d@att.net> <8tvqbseHeL7Rg95afREMiE05bGM@jntp> <c574a8da-34ec-4f1e-9169-1f85a39b69b8@att.net> <v06beh$13pd1$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 22 Apr 2024 21:36:14 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="024b8cce0d80bd384762a74093bceceb"; logging-data="1192824"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+rVQaF6MAjiz9YL+UAXFNkNgeC12lgO3o="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:0m0KxrV8QxcjcALgtlSCXwLG1gA=
In-Reply-To: <v06beh$13pd1$1@dont-email.me>
Content-Language: en-US
Xref: csiph.com sci.math:627104

On 4/22/2024 2:48 PM, Moebius wrote:
> Am 22.04.2024 um 19:32 schrieb Jim Burns:

>> ⦅0,ω+ω⦆ fits ⦅0,ω⦆
>
> Def:
> (u, v) := {x e ORD : u < x < v}
> (with x,y e ORD)
>
> Then ⦅0,ω⦆ c ⦅0,ω+ω⦆, but not ⦅0,ω+ω⦆ c ⦅0,ω⦆.
>
> After all, ω < ω+1 < ω+2 < ... < ω+ω.
>
> So with "I fits J",
> you don't mean "I fits in J",
> but rather "J fits in I", I guess.
> Right?
>
> A commen term in this context is "contains".
> Hence ⦅0,ω+ω⦆ contains ⦅0,ω⦆.

I am using "fit" differently.
X fits Y  ⟺  X [≤] Y  ⟺
exists 1.to.1 f: X ⇉ Y

Yes
ω < ω+1 < ω+2 < ... < ω+ω
However,
ω [≤≥] ω+1 [≤≥] ω+2 [≤≥] ... [≤≥] ω+ω
ω [=] ω+1 [=] ω+2 [=] ... [=] ω+ω

The distinction I make for WM is
κ [≤≱] κ+1 [≤≱] ... ω [≤≥] ω+1 [≤≥] ...
κ [<] κ+1 [<] ... ω [=] ω+1 [=] ...


I'm sorry for the confusion.
I am trying to shorten my posts enough that
WM will read them.
I am an eternal optimist.

The stylistic choice I make is a two.edged sword.
I feel it is a dynamic, very.readable style,
leaning toward the Ernest.Hemingway.ish.
However, deleting context courts confusion,
as you have noticed.