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From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: Simply defining =?utf-8?Q?G=C3=B6del?= Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined)
Date: Fri, 24 Jul 2020 16:11:34 -0700
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David Kleinecke <dkleinecke@gmail.com> writes:
> On Friday, July 24, 2020 at 3:45:44 PM UTC-7, olcott wrote:
>> On 7/24/2020 5:38 PM, David Kleinecke wrote:
>> > On Friday, July 24, 2020 at 2:01:03 PM UTC-7, olcott wrote:
>> >>
>> >> I haven't the time to read a whole book to answer one trivial question:
>> >> Is this a correct way to encode a set of ordered pairs:
>> >> {(3,9),(8,5),(8,9)}
>> >   
>> > Close enough that no one will complain.
>> > 
>> > I'd leave out all the commas
>> >      {(3 9) (8 5) (8 9)}
>> > Many people prefer square brackets
>> >      {[3 9] [8 5] [8 9]}
>> > A set of unordered pairs would be
>> >      {{3 9} {8 5} {8 9}}
>> > 
>> > Note the spaces in those formulas matter.
>> > 
>> 
>> Mendelson uses some kind of angle-bracket: <3,7> yet with an angle that 
>> is much less sharp. Wikipedia specifies (3,7). No where have I seen 
>> leaving out the commas of a single ordered pair.
>  
> Lots of notations exist. You can invent your own - provided
> you explain how it works. 
>
> Another possibility is writing the ordered pair of a and y
> as x ORD y and unordered sets as x UN y then
>     3 ORD 9 UN 8 ORD 5 UN 8 ORD 9
> I don't recommend that one - but it's not wrong.

It would benefit from a specificatior of operator precedence.

> Mendelson, I assume, worked up a uniform style for his
> whole book and used it consistently. I am just making
> up notations on the fly for nonce use.
>
> I think it was Gauss who said "We need notions not
> notations." 

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips Healthcare
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