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Re: Conclusion
Posted:
Nov 7, 2012 9:09 AM
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On Nov 7, 6:53 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> Dan Christensen <Dan_Christen...@sympatico.ca> writes:
> > On Nov 6, 6:18 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> >> You didn't say that. You said earlier today that composition was not
> >> functional.
>
> > [snip]
>
> > Pay attention, Jesse. In every version of my definition of category,
> > composition was presented as a function. For every ordered pair of
> > compatible morphisms, there would exist a unique morphism that was
> > their composition. After posting my latest version, I began to openly
> > question it here, wondering if indeed such a unique morphism always
> > existed. It doesn't always, but, as Aatu pointed out in effect, you
> > arbitrarily pick one of the alternatives for your definition of
> > compositions to maintain functionality -- "We flip a coin." So, my
> > latest definition of stood.
>
> Wow. You are either a liar or have a mental condition that represses
> all memory of your errors.
>
> Look at message https://groups.google.com/group/sci.math/msg/87d7499de8ad28de?dmode=s...
> Message-ID: <60c69813-35f2-4bc7-8fb2-f81b8e0ea9f7@h9g2000yqd.googlegroups.com>
>
> Here, we find axiom 2:
>
> 2 ALL(f):ALL(g):ALL(h):[f @ mor & g @ mor & h @ mor => [(f,g,h) @
> comp
> <=> cod(f)=dom(g) & dom(f)=dom(h) & cod(h)=cod(g)]]
>
A little creative editing, Jesse? In the text just prior to that (see
link), I wrote:
"I also think there may be a larger problem with the functionality of
composition. Suppose, for example, that f is morphism from object A to
object B, that g is morphism from B to C, and that h1 and h2 are
distinct morphisms from A to C. Then comp(g,f) as defined here could
be either h1 or h2, could it not? Should we define some equivalence
relation on mor. Should comp be seen as a non-functional mapping from
mor x mor to mor? How about something like..."
Aatu, it seems, kicked your ill-informed butt with his "We flip a
coin" remark. You no longer claim I was "lying" about that. That's
real progress. But here, it seems you are reduced to deliberately
taking my words out of context and, again, calling me a liar!
In your desperate, never-ending attempts to make me look stupid, it
seems to have backfired on you, Jesse.
Now, about those massive insecurities....
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
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