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

From	Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups	comp.theory
Subject	Re: How to define '=' in expression "a=b"?
Date	2021-07-19 16:06 +0100
Organization	A noiseless patient Spider
Message-ID	<8735sajqc8.fsf@bsb.me.uk> (permalink)
References	<067463e7-6234-4bff-954f-80183e637b51n@googlegroups.com>

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wij <wyniijj@gmail.com> writes:

> 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?

It's a big topic, but any book on formal logic will explain the
definition used in first order theories.  You'll also find an
explanation of bound and free variables which is key to correctly
defining substitution in formulas.

-- 
Ben.

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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