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Re: Results of Poll by Email No. 27

From: Robert B Wilson Wednesday, April 9, 2003, 12:19
```On Wed, 9 Apr 2003 12:26:37 +0200 Christian Thalmann <cinga@...>
writes:
> --- In conlang@yahoogroups.com, Robert B Wilson <han_solo55@J...>
> wrote:
>  > 0/0={0,1} (actually it's not really that simple, 0/0 isn't
> considered to
>  > have two values, but one that is 0 and 1 at the same time (this
> type of
>  > value is called called a _luatkarno_ [4M?@skar\no]))
>  >
>  > 5*0/0={0,1},{0,5}
>
> I don't get it.  If 0/0 = {0,1}, shouldn't 5*0/0 = {0,5}?
> What does the comma between the braces mean?
5*0/0=both {0,1} and {0,5}:
(5*0)/0=0/0={0,1}
5*(0/0)=5*{0,1}={0,5}

>  > 2*5*0/0={0,1},{0,10}
>  > 1+5*0/0={0,1},{1,6}
>
> Hunh?  Is that (1+5)*0/0 or 1+(5*0/0)?  In the latter
> case, I'd just expect {1,6}...  again, what's the
> first part of the result supposed to mean?
the first part of the result is what you get when you take it as
(whatever*0)/0=0/0={0,1}

>  > 1/0=1+0/0={0,1},{1,2}
>
> Wait a second...  1/0 = (1+0)/0, certainly, but is
> 1/0 = 1+(0/0)?  I don't see why it should...oops... i guess i made a mistake there... hmm... what would 1/0 equal? i
don't want to just say inf cause then you can't just multiply it by 0 and
get 1 (5/0 would be inf also (5inf=inf))...

>  > {0,1}/{0,1}={0,0}=0
>
> Eh?  Shouldn't that end up as 1?
no... things get sort of complicated when dealing with these
_luatkarno_'s (i haven't figured out what should be the plural of this
word (or if it should be the same as the singular...)

>  > {0,5}/{0,1}=5
>
> That's inconsistent with {0,1}/{0,1}=0.
well, {0,1} behaves a little differently (sort of like 0 behaves a little
differently from other numbers)

>  > {0,10}/{0,1}=10
>  > {1,6}/{0,1}=6
>  > {1,2}-{0,1}={1,1}=1
>
> That's a bit problematic...
not really... it's consistent

hmm... i'm having a rather hard time figuring all this out...

>         0 = 0
>     ==> y * 0 = x * 0                   | /0
>     ==> y * {0,1} = x * {0,1}
>     ==> {0,y} = {0,x}                   | /{0,1}
>     ==> {0,y} / {0,1} = {0,x} / {0,1}
>     ==> y = x
>
> Since x and y were arbitrary, x = y for all x, y.
>
> There's a reason why we don't divide by zero, you know. ;-)
> Anyway, if you want to assign a value to 1/0, better use
> infinity.  It makes more sense, seeing how 1/x -> inf for
> x -> 0.  (Incidentally, that goes for positive as well as
> negative approaches to 0, so inf = -inf.)  Just don't allow
> things like 0/0, inf-inf, inf/inf, 0*inf or such be
> evaluated without deeper thought.  That will only ride you
hmm... it all makes sense if you allow statements to be true and false at
the same time...

>  > any ideas how i can get a computer to do this sort of thing?
>
> Use an object class for your numbers, and define methods
> for all operations you'd like to be able to do.  However,