Subject: Re: [lojban] periodic hexadecimal reminder

From: "Bob LeChevalier (lojbab)" <[email-masked]>
Date: Fri, 28 Sep 2001 21:06:51 -0400

At 05:00 PM 9/26/01 -0400, John Cowan wrote:
>Pierre Abbat wrote:
> > I think {ju'u} is in the wrong selma'o. All other binary mex operands take
> > two numbers and return a number.

Not necessarily. That may be the most common usage. But "addition" in the 
context of non-numerical strings is usually interpreted as concatenation, 
and Mex is used to handle that as well. Mex allows all manner of 
operations, including operations on objects not normally considered to be 
mathematical. In Lojban you really can compare apples and oranges (using 
Mex). All you have to do is define what the basis for the comparison 
is. (In slot machines, a cherry is greater than a lemon.)

> >{ju'u} takes a naclerpoi and a number and
> > returns a number.

That is the standard mathematical application of ju'u. But when I was 
looking into Mex, I found all manner of strange notations and operations 
that might be portrayed using Mex.

> > ze bi'esu'i bi pi'i so = (7+8)*9
> > ze bi'esu'i bi ju'u so = ?
> > is it 14 (which is written 15 in base 9) or what?
>
>It's nonsense.

I'm not sure I agree; rather it is moot. I understand (a+b) base c to mean 
evaluate (a+b) assuming each is written in base c. It is only "nonsense" 
because there is no reason to have used the bi'e since there is no standard 
mathematical usage where different bases would be used for different 
numbers without explicitly marking them so that 7 + 8base9 implicitly means 
7 base 9 + 8 base 9.

Lojban does not purport to dictate the semantics of mathematics, which is 
self consistent only within a single axiomatic context.

--
lojbab [email-masked]
Bob LeChevalier, President, The Logical Language Group, Inc.
2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
Artificial language Loglan/Lojban: http://www.lojban.org