Deutsch   English   Français   Italiano  
<vat7g8$k90v$1@dont-email.me>

View for Bookmarking (what is this?)
Look up another Usenet article

Path: ...!feeds.phibee-telecom.net!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Jeff Barnett <jbb@notatt.com>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Fri, 30 Aug 2024 13:45:09 -0600
Organization: A noiseless patient Spider
Lines: 107
Message-ID: <vat7g8$k90v$1@dont-email.me>
References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <va4h96$3r7nv$1@dont-email.me>
 <H5iV5HXUBwUzWtVKRZj7h4N2LdA@jntp> <va543m$3u6dp$1@dont-email.me>
 <kN73KZJabPuiasJJ0DR6UOOrMHE@jntp>
 <d47ad77b3f2bd0bc6280b8eca772b280f3a18dc8@i2pn2.org>
 <ivRRwss8WgoMTIfJa5g04TJmRxU@jntp>
 <db885c7c1e1a5bfdf60e90fa9882bfb73b4e6ce7@i2pn2.org>
 <eY2Memk56jLKsrTeR3kBDQQqfHI@jntp>
 <bdfbb725-7fc3-4e17-b09b-4d6191d301a5@att.net>
 <tvUGDEKZBjBIOn4R0HIJvG5es4k@jntp>
 <aab21a74-45e2-4a91-835f-d6aa2adeb7ff@att.net> <vansci$3j3d7$1@dont-email.me>
 <adb8b04c-8fb0-4a96-8d4a-d04bda37a5af@att.net> <vaomrb$3qgik$1@dont-email.me>
 <73630f48-a854-46bd-a17b-05b6c246e0fd@att.net> <varhba$blb9$1@dont-email.me>
 <vat6gf$k5jd$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: base64
Injection-Date: Fri, 30 Aug 2024 21:45:13 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="c97717bccb4632a585a8f1eb47f0b6fc";
	logging-data="664607"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/dskeNrpfmfWwX0Jn2pD4q8B6p7vWEFsM="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:piPEihTTF/g0Q4eTXCMSgAHtQcc=
Content-Language: en-US
In-Reply-To: <vat6gf$k5jd$3@dont-email.me>
X-Antivirus: AVG (VPS 240830-4, 8/30/2024), Outbound message
X-Antivirus-Status: Clean
Bytes: 9699

T24gOC8zMC8yMDI0IDE6MjggUE0sIENocmlzIE0uIFRob21hc3NvbiB3cm90ZToNCj4gT24g
OC8yOS8yMDI0IDk6MjAgUE0sIEplZmYgQmFybmV0dCB3cm90ZToNCj4+IE9uIDgvMjkvMjAy
NCAyOjA5IFBNLCBKaW0gQnVybnMgd3JvdGU6DQo+Pj4gT24gOC8yOC8yMDI0IDEwOjM2IFBN
LCBKZWZmIEJhcm5ldHQgd3JvdGU6DQo+Pj4+IE9uIDgvMjgvMjAyNCAyOjEwIFBNLCBKaW0g
QnVybnMgd3JvdGU6DQo+Pj4NCj4+Pj4+IFsuLi5dDQo+Pj4+DQo+Pj4+ICJUcmljaG90b21v
dXMiIGdlbmVyYXRlcyB0aGUgcmlnaHQgbWVudGFsIGltYWdlcywNCj4+Pj4gSSBtdXN0IGFk
bWl0Lg0KPj4+PiBCdXQgSSdtIG5vdCBzdXJlIGhvdyBvbmUgY291bGQgc2hvdyB0aGF0DQo+
Pj4+IGEgcmVsYXRpb24gUiBvbiBTLCB3aGVyZSBSIGlzIFRyaWNob3RvbW91cywNCj4+Pj4g
aW1wbGllcyB0aGF0DQo+Pj4+IEkgY2FuJ3QgMS0xIG1hcCBhIHN0cmljdCBzdWJzZXQgb2Yg
UiB0byBSLg0KPj4+DQo+Pj4gSSBhZ3JlZSB0aGF0IG9uZSBjYW4ndCBwcm92ZSB0aGF0Lg0K
Pj4+IEkgYW0gZG9pbmcgc29tZXRoaW5nIGVsc2UgaGVyZS4NCj4+Pg0KPj4+DQo+Pj4gTXkg
YXBvbG9neSBmb3IgaGF2aW5nIHN0cmlwcGVkIHNvIG11Y2ggY29udGV4dC4NCj4+PiBJIGdl
dCBjb21wbGFpbnRzIGFib3V0IHRoZSBsZW5ndGggb2YgbXkgcG9zdHMuDQo+Pj4NCj4+PiBB
bmQsIGFzIG11Y2ggYXMgc3RyaXBwaW5nIGNvbnRleHQgaXMgbm90IHRvIG15IHRhc3RlLA0K
Pj4+IGlmIG15IGNoaWVmIGNvcnJlc3BvbmRlbnQgd29uJ3QgcmVhZCBteSBicmlsbGlhbnQg
dGV4dCwNCj4+PiBTb21ldGhpbmcgTXVzdCBCZSBEb25lLg0KPj4+DQo+Pj4gVGhlIFNvbWV0
aGluZyB3aGljaCBNdXN0IEJlIERvbmUgaXMgdGhhdA0KPj4+IG15IHNpZGUgb2YgdGhpcyBt
dWx0aS55ZWFyIGNvcnJlc3BvbmRlbmNlIGhhcyBiZWNvbWUNCj4+PiBhIHNlYXJjaCBmb3Ig
cGVyZmVjdCB6aW5nZXJzIGJ5IHdoaWNoIHRvIHRyYW5zbWl0DQo+Pj4gcHJpbmNpcGxlcyBv
ZiBwcmVkaWNhdGUgbG9naWMsIGZpbml0ZW5lc3MsIGluZmluaXRlbmVzcywNCj4+PiBzZXRz
LCBuYXR1cmFsIG51bWJlcnMsIHJlYWwgbnVtYmVycywgYW5kIG90aGVyIHRvcGljcywNCj4+
PiBhcyBhcHByb3ByaWF0ZS4NCj4+Pg0KPj4+IFRoZSBzZWFyY2ggZm9yIHppbmdlcnMgaGFz
IGtlcHQgbWUgdG9sZXJhYmx5IGFtdXNlZCwNCj4+PiBzbyBmYXIsIGVub3VnaCB0byBrZWVw
IG1lIHBsdWdnaW5nIGF3YXksIGF0IGxlYXN0Lg0KPj4+IFRoZSBkb3duc2lkZSBpcyB0aGF0
IGEgcmFuZG9tIHBhc3NlcmJ5LCBzdWNoIGFzIHlvdXJzZWxmLA0KPj4+IG1pZ2h0ICh1bmRl
cnN0YW5kYWJseSkgZmluZCB3aGF0ZXZlci53ZS5oYXZlLmhlcmUgb3BhcXVlLg0KPj4+IEFn
YWluLCBteSBhcG9sb2d5Lg0KPj4+DQo+Pj4gQ29udGV4dDoNCj4+Pg0KPj4+IFdvbGZnYW5n
IE3DvGNrZW5oZWltIGhhcyBiZWVuIHJlamVjdGluZw0KPj4+IERlZGVraW5kLmluZmluaXRl
IHNldHMsIHNldHMgUiBzdWNoIHRoYXQNCj4+PiBJIGNhbiAxLTEgbWFwIGEgc3RyaWN0IHN1
YnNldCBvZiBSIHRvIFIuDQo+Pj4gV00gY2FsbHMgdGhlbSAicG90ZW50aWFsbHkgaW5maW5p
dGUiLCBieSB3aGljaA0KPj4+IFdNIG1lYW5zIHRoYXQgdGhlc2Ugc2V0cyBjaGFuZ2UsIHdo
aWNoIG1lYW5zIHRoYXQNCj4+PiBXTSBpcyBub3QgdGFsa2luZyBhYm91dCBfdGhvc2Ugc2V0
c18NCj4+PiB3aGljaCBkbyBub3QgY2hhbmdlLg0KPj4+DQo+Pj4gQSB0eXBpY2FsIFdNLmFy
Z3VtZW50IHNldHMgdXAgc29tZSBzZXF1ZW5jZSBhbmQNCj4+PiBhc3NlcnRzIGJ5IG1hdGhl
bWF0aWNzLCBieSBsb2dpYw0KPj4+IChpbiByZWFsaXR5LCBieSAiY29tbW9uIHNlbnNlIiwg
YnkgIm9idmlvdXNuZXNzIikNCj4+PiB0aGF0IHRoZSBzZXF1ZW5jZSBoYXMgdHdvIGVuZHMu
DQo+Pj4gU2luY2UgdGhlIHNlcXVlbmNlIGhhcyBvbmx5IG9uZSBfdmlzaWJsZV8gZW5kLA0K
Pj4+IFdNIGNvbnNpZGVycyB0aGF0IHByb29mIG9mIGEgc2Vjb25kIGVuZCB3aGljaCBpcyBf
ZGFya18NCj4+Pg0KPj4+IEl0IGlzIGFuIGFyZ3VtZW50IHdoaWNoIGZvY3VzZXMgb24gc2Vx
dWVuY2VzLg0KPj4+DQo+Pj4gVGhlcmUgaXMgYW5vdGhlciBkZWZpbml0aW9uIG9mIGZpbml0
ZW5lc3MvaW5maW5pdGVuZXNzDQo+Pj4gd2hpY2ggZG9lc24ndCBpbW1lZGlhdGVseSBjYWxs
IGZvciBEZWRla2luZC5pbmZpbml0ZSBzZXRzDQo+Pj4gYW5kIHdoaWNoIGRvZXMgZm9jdXMg
b24gc2VxdWVuY2VzLg0KPj4+IOKOmyBBIGZpbml0ZSBzZXQgaGFzIGFuIG9yZGVyIHdoaWNo
IGlzIHdlbGwub3JkZXJlZA0KPj4+IOKOnCBpbiBib3RoIGRpcmVjdGlvbnMuDQo+Pj4g4o6d
IC0tIFBhdWwgU3TDpGNrZWwsIDE4NjIuLi4xOTE5DQo+Pj4NCj4+PiBJIGhhdmUgYmVlbiBy
ZS5kZXJpdmluZyBmYW1pbGlhciAodG8gdXMpIHJlc3VsdHMNCj4+PiBmb3IgU3TDpGNrZWwu
ZmluaXRlIGFuZCBTdMOkY2tlbC5pbmZpbml0ZSBzZXRzLCBpbnN0ZWFkIG9mDQo+Pj4gZm9y
IERlZGVraW5kLmZpbml0ZSBhbmQgRGVkZWtpbmQuaW5maW5pdGUgc2V0cy4NCj4+Pg0KPj4+
ICdTdMOkY2tlbC5maW5pdGUnIGlzIG1lc3NpZXIuDQo+Pj4gSSBmcmFtZSBpdCBpbiB0ZXJt
cyBvZiBTdMOkY2tlbC5maW5pdGUgb3JkZXJzIGFuZA0KPj4+IFN0w6Rja2VsLmluZmluaXRl
IG9yZGVycywgYnV0IHdoYXQgZG8gd2Ugc2F5IGFib3V0DQo+Pj4gc2V0cyB3aGljaCBoYXZl
IGJvdGg/DQo+Pj4NCj4+PiBNeSBhbnN3ZXIgdG8gdGhhdCBpcyB3aGF0IHlvdSwgUmFuZG9t
IFBhc3NlcmJ5LA0KPj4+IGhhdmUgYmVmb3JlIHlvdSwgaGVyZS4NCj4+Pg0KPj4+IExlbW1h
Lg0KPj4+IOKOmyBBIHNldCBjYW5ub3QgaGF2ZSBib3RoIGEgU3TDpGNrZWwuZmluaXRlIG9y
ZGVyIGFuZA0KPj4+IOKOnSBhIFN0w6Rja2VsLmluZmluaXRlIG9yZGVyLg0KPj4+DQo+Pj4g
VGhhdCdzIHdoYXQgSSBwcm92ZSwgd2hpY2ggYWxsb3dzIG1lIHRvIG1lIHRvIG9mZmVyDQo+
Pj4gYSBjbGVhcmVyIChvciBhdCBsZWFzdCBhIGRpZmZlcmVudCkgdmlldyBvZg0KPj4+IGZp
bml0ZW5lc3MgYW5kIGluZmluaXRlbmVzcy4NCj4+Pg0KPj4+PiBCdXQgSSdtIG5vdCBzdXJl
IGhvdyBvbmUgY291bGQgc2hvdyB0aGF0DQo+Pj4+IGEgcmVsYXRpb24gUiBvbiBTLCB3aGVy
ZSBSIGlzIFRyaWNob3RvbW91cywNCj4+Pj4gaW1wbGllcyB0aGF0DQo+Pj4+IEkgY2FuJ3Qg
MS0xIG1hcCBhIHN0cmljdCBzdWJzZXQgb2YgUiB0byBSLg0KPj4+DQo+Pj4gQW5kIEkgZG9u
J3Qgc2hvdyB0aGF0Lg0KPj4+DQo+Pj4gSSBzaG93IHRoYXQsDQo+Pj4gaWYgb25lIG9yZGVy
IG9mIEIgaXMgU3TDpGNrZWwuZmluaXRlDQo+Pj4gYW5kIGEgc2Vjb25kIG9yZGVyIGlzIHRy
aWNob3RvbW91cywNCj4+PiB0aGVuIHRoZSBzZWNvbmQgb3JkZXIgaXMgYWxzbyBTdMOkY2tl
bC5maW5pdGUuDQo+Pj4NCj4+PiBUaHVzLA0KPj4+IGJlY2F1c2Ug4oSVIGhhcyBhIHN0YW5k
YXJkIG9yZGVyIHdpdGggb25lIGVuZCwNCj4+PiB0aGVyZSBpcyBubyBTdMOkY2tlbC5maW5p
dGUgb3JkZXIgb2Yg4oSVLg0KPj4+IFRoZXJlIGlzIG5vIHN1cGVyc2V0IG9mIOKElSB3aXRo
IGEgU3TDpGNrZWwuZmluaXRlIG9yZGVyLA0KPj4+IGVpdGhlci4NCj4+DQo+PiBJJ3ZlIHB1
dCBteSBub3NlIGludG8gYSBmZXcgb2YgdGhlIHNhbWUgbmV3c2dyb3VwcyB0aGF0IHlvdSBo
YXZlIGFuZCBJIA0KPj4gYW0gYXdhcmUgb2YgdGhlIGFyb21hLiBJIG5vIGxvbmdlciBldmVu
IHRoaW5rIGFib3V0IGludGVyYWN0aW5nIHdpdGggDQo+PiBXTSwgUE8sIG9yIGEgZmV3IG90
aGVycyBjdXQgZnJvbSB0aGUgc2FtZSBzYWQgY2xvdGguIE9mIGNvdXJzZSBJIA0KPj4gb2Nj
YXNpb25hbGx5IHBvc3Qgc29tZXRoaW5nICphYm91dCogdGhlbS4gVGhlcmUgYXJlIHNldmVy
YWwgDQo+PiBwb3NzaWJpbGl0aWVzIGZvciB0aGUgV00gb2YgdGhlc2UgdGhyZWFkczogMSkg
SGUncyBhbiBpZGlvdDsgMikgSGUncyANCj4+IGV4dHJlbWVseSBsb25lc29tZSBhbmQgdGhl
c2UgaW50ZXJhY3Rpb25zIHBhc3MgZm9yICJiZWluZyBlbmdhZ2VkIjsgMykgDQo+PiBIZSdz
IG5vdCB3aG8gaGUgY2xhaW1zIHRvIGJlIChhbiBpbnN0cnVjdG9yIGF0IGEgKGp1bmlvcj8p
IGNvbGxlZ2UpOyANCj4+IDQpIGhlJ3Mgc2ltcGx5IGFuIG91dHJpZ2h0IHRyb2xsOyA1KSBI
ZSdzIHJlbGlnaW91czsgNikgSGUncyANCj4+IGRlbHVzaW9uYWwuIE9mIGNvdXJzZSBhbnkg
c3Vic2V0IG9mIHRoZXNlIGlzIHBvc3NpYmxlLg0KPiANCj4gQSBtYXNzaXZlIHRyb2xsIHRo
ZSBlbmNvbXBhc3NlcyBhbGwgb2YgaXQ/IFRoZSBzY2FyeSBwYXJ0IGlzIHRoYXQgaGUgaXMg
DQo+IGEgdGVhY2hlci4gQWN0dWFsbHksIGlzIHRoYXQgZXZlbiB0cnVlPw0KDQpOdW1iZXIg
MyBhYm92ZSBsaXN0cyB0aGF0IGFzIG9uZSBwb3NzaWJpbGl0eS4gSXQncyBsaWtlIGFza2lu
ZyBpZiBQTyANCih0aGUgY3VsdHVyZWQgaWRpb3QgaW4gc28gbWFueSBvdGhlciBtYXRoIGFu
ZCBsb2dpYyBncm91cHMpIGlzIHJlYWxseSANCnRoZSBwZWRvcGhpbGUgb2YgYSBjb3VydCBj
YXNlIGtub3duIG9uIHRoZSBuZXQgb3IganVzdCBhbiBpZGVudGl0eSANCnBpY2tlZCB0byBp
bmZsYW1lIGhpcyBjb250ZXN0YW50cy4gVHJhY2tpbmcgZG93biBhbmQgVkVSSUZZSU5HIGFu
IA0KaWRlbnRpdHkgZnJvbSB0aGUgaGVhZGVyIG9mIGFuIGVtYWlsIGlzIHJlYWxseSBkaWZm
aWN1bHQuIEJvdGggV00gYW5kIFBPIA0KbGllIGFib3V0IHNvIG11Y2ggdGhhdCBpdHMgaGFy
ZCB0byBiZSBzdXJlIHdobyB0aGV5IGFyZS4gVGhlIG9ubHkgdGhpbmdzIA0KSSBndWVzcyBm
cm9tIHRoZWlyIGNvcGlvdXMgbmV0IHByZXNlbmNlcyBpcyB0aGF0IGJvdGggYXJlIGxvbmVz
b21lIGFuZCANCmhhdmUgbGl0dGxlIGh1bWFuIHRvIGh1bWFuIGNvbnRhY3QuDQoNCj4+IElu
IGFueSBldmVudCBubyBpbnRlcmFjdGlvbnMgd2l0aCBoaW0gd2lsbCBjaGFuZ2UgaGlzIGJl
aGF2aW9yIC0tIHRoYXQgDQo+PiBpcyBvbmUgb2YgaGlzIG1vc3QgaW50ZXJlc3Rpbmcgc2lt
aWxhcml0aWVzIHRvIFBPLiBJdCdzIHJlYWxseSB0b28gYmFkIA0KPj4gdGhhdCBzb21lIG5l
d3Nncm91cHMgdGhhdCB3ZXJlIGJvdGggaW50ZXJlc3RpbmcgYW5kIGVkdWNhdGlvbmFsIGhh
dmUgDQo+PiBmYWxsZW4gc28gZmFyLiBJIHJlbWVtYmVyIHRoZSBncmVhdCBob3BlcyB3ZSBh
bGwgaGFkIGJhY2sgaW4gdGhlIGxhdGUgDQo+PiAxOTYwcyBhbmQgZWFybHkgMTk3MHMgZm9y
IGEgZGlmZmVyZW50LCBiZXR0ZXIgaW5mb3JtZWQsIGFuZCBqdXN0IHBsYWluIA0KPj4gYmV0
dGVyIHdvcmxkIGJlY2F1c2Ugb2YgdGhlIHN1cHBvcnRhYmxlIHZpc2lvbiB0aGUgQVJQQSBy
ZXNlYXJjaCBuZXQgDQo+PiBzZWVtZWQgdG8gb2ZmZXIuDQo+Pg0KPj4gV2hhdCB3ZSBhbGwg
Zm9yZ290IHdhcyB0aGUgb2xkIHdpc2RvbSB0aGF0IHN0YXRlZCAiQ2hhcmFjdGVyIC8gZXRo
aWNzIA0KPj4gLyBwZXJzb25uZWwgd29ydGggLyBzb3VsIC8gZXRjLiBpcyB3aGF0IHlvdSBh
cmUgd2hlbiBubyBvbmUgY2FuIHNlZSANCj4+IHlvdS4gVW5mb3J0dW5hdGVseSB0aGUgaW50
ZXJuZXQgbWFkZSB0aGUgbWFnaWMgc2hpZWxkIHRoYXQgZXhwb3NlZCBhbGwgDQo+PiBvZiBo
dW1hbiBuYXN0aW5lc3Mgd2hpbGUgbWFza2luZyB0aGUgZmFjZXMgb2YgdGhlIHBlcnBldHJh
dG9ycy4NCi0tIA0KSmVmZiBCYXJuZXR0DQoNCg==