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 21:45 +0100
Organization	A noiseless patient Spider
Message-ID	<87wnpmhw1w.fsf@bsb.me.uk> (permalink)
References	<067463e7-6234-4bff-954f-80183e637b51n@googlegroups.com> <8735sajqc8.fsf@bsb.me.uk> <13985d26-7898-4658-9084-ecb836097df3n@googlegroups.com>

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wij <wyniijj@gmail.com> writes:

> On Monday, 19 July 2021 at 23:06:18 UTC+8, Ben Bacarisse wrote:
>> wij <wyn...@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. 
>> 
> I quickly scanned all possible books related to your "formal logic",...none.
> The '=' is basically used unexplained.

I suggest a slower scan.

-- 
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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