Re: How to define '=' in expression "a=b"?

From	Peter <peterxpercival@hotmail.com>
Newsgroups	comp.theory
Subject	Re: How to define '=' in expression "a=b"?
Date	2021-07-19 18:28 +0100
Organization	Aioe.org NNTP Server
Message-ID	<sd4cns$m78$1@gioia.aioe.org> (permalink)
References	<067463e7-6234-4bff-954f-80183e637b51n@googlegroups.com>

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wij wrote:
> Definition of equal sign '=' (mathematics ):
> 1. Basic definition: a=b iff a and b are exchangeable
> 2. For any? equation X=Y, the occurrence of a,b in X,Y are exchangeable
> 
> Any suggestion improving the definition of '=' in mathematical expression?
> (The axiom of extension in set theory is not appropriate, because it is set only)
> 

If everything is a set then "set only" is not a limitation!

One definition of identity is that two things are identical if 
everything true of one is true of the the and vice versa.

Substitution can be a problem.  Consider -

(i) The morning star is identical to the evening star. (True, for both 
are the plant Venus.)
(ii) Fred believes that the morning star is Venus.

 From those, if exchangeability holds, one could conclude Fred believes 
that the evening star is Venus.  But that may not be so.

-- 
The world will little note, nor long remember what we say here
Abraham Lincoln at Gettysburg

Thread

How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-18 18:21 -0700
  Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-19 08:00 -0700
  Re: How to define '=' in expression "a=b"? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-19 16:06 +0100
    Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-19 10:24 -0700
      Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-19 18:44 +0100
        Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-19 18:28 -0700
          Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-22 13:22 +0100
            Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-22 07:25 -0700
              Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-22 17:20 +0100
      Re: How to define '=' in expression "a=b"? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-19 21:45 +0100
        Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-19 18:30 -0700
          Re: How to define '=' in expression "a=b"? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 11:18 +0100
      Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:26 -0700
        Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-22 09:41 -0700
    Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:19 -0700
    Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:51 -0700
      Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:52 -0700
  Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-19 18:28 +0100
    Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-19 18:27 -0700
      Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:30 -0700
    Re: How to define '=' in expression "a=b"? Charlie-Boo <shymathguy@gmail.com> - 2021-07-22 08:23 -0700
  Re: How to define '=' in expression "a=b"? Jeff Barnett <jbb@notatt.com> - 2021-07-19 14:41 -0600
    Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-19 19:52 -0700
      Re: How to define '=' in expression "a=b"? Jeff Barnett <jbb@notatt.com> - 2021-07-19 22:04 -0600
        Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-21 20:14 -0700
      Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-22 13:24 +0100
        Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-22 07:26 -0700
          Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-22 17:16 +0100
  Re: How to define '=' in expression "a=b"? olcott <NoOne@NoWhere.com> - 2021-07-22 10:17 -0500
    Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-22 09:31 -0700
      Re: How to define '=' in expression "a=b"? olcott <NoOne@NoWhere.com> - 2021-07-22 11:44 -0500
        Re: How to define '=' in expression "a=b"? wij <wyniijj@gmail.com> - 2021-07-22 09:52 -0700
          Re: How to define '=' in expression "a=b"? olcott <NoOne@NoWhere.com> - 2021-07-22 12:01 -0500
            Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-22 19:13 +0100
              Re: How to define '=' in expression "a=b"? Richard Damon <Richard@Damon-Family.org> - 2021-07-22 11:24 -0700
              Re: How to define '=' in expression "a=b"? [ Gödel as Tarski ] olcott <NoOne@NoWhere.com> - 2021-07-24 13:18 -0500
            Re: How to define '=' in expression "a=b"? Peter <peterxpercival@hotmail.com> - 2021-07-24 18:57 +0100
              Re: How to define '=' in expression "a=b"? Jeff Barnett <jbb@notatt.com> - 2021-07-24 12:12 -0600
                Re: How to define '=' in expression "a=b"? olcott <NoOne@NoWhere.com> - 2021-07-24 13:33 -0500
                Re: How to define '=' in expression "a=b"? Jeff Barnett <jbb@notatt.com> - 2021-07-24 15:56 -0600
                Re: How to define '=' in expression "a=b"? olcott <NoOne@NoWhere.com> - 2021-07-24 17:05 -0500
                Re: How to define '=' in expression "a=b"? Jeff Barnett <jbb@notatt.com> - 2021-07-24 16:13 -0600
                Re: How to define '=' in expression "a=b"? Richard Damon <Richard@Damon-Family.org> - 2021-07-24 19:52 -0700
              Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] olcott <NoOne@NoWhere.com> - 2021-07-24 13:27 -0500
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] Peter <peterxpercival@hotmail.com> - 2021-07-25 12:59 +0100
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] olcott <NoOne@NoWhere.com> - 2021-07-25 10:13 -0500
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] André G. Isaak <agisaak@gm.invalid> - 2021-07-25 09:55 -0600
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] olcott <NoOne@NoWhere.com> - 2021-07-25 11:23 -0500
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] André G. Isaak <agisaak@gm.invalid> - 2021-07-25 10:51 -0600
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] olcott <NoOne@NoWhere.com> - 2021-07-25 12:02 -0500
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] André G. Isaak <agisaak@gm.invalid> - 2021-07-25 11:40 -0600
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] olcott <NoOne@NoWhere.com> - 2021-07-25 13:05 -0500
                Re: How to define '=' in expression "a=b"? ? [ Gödel as Tarski ] André G. Isaak <agisaak@gm.invalid> - 2021-07-25 13:07 -0600
        Re: How to define '=' in expression "a=b"? Richard Damon <Richard@Damon-Family.org> - 2021-07-22 10:28 -0700

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