Fwd: [Haskell-cafe] Category Theory woes

[Nick Rudnick]

Hi Mike,

so an open set does not contain elements constituting a border/boundary 
of it, does it?

But a closed set does, doesn't it?

Cheers,

    Nick

Michael Matsko wrote:
>
> ----- Forwarded Message -----
> From: "Michael Matsko" <msmatsko at comcast.net>
> To: "Nick Rudnick" <joerg.rudnick at t-online.de>
> Sent: Thursday, February 18, 2010 2:16:18 PM GMT -05:00 US/Canada Eastern
> Subject: Re: [Haskell-cafe] Category Theory woes
>
> Gregg,
>
>  
>
>    Topologically speaking, the border of an open set is called the 
> boundary of the set.  The boundary is defined as the closure of the 
> set minus the set itself.  As an example consider the open interval 
> (0,1) on the real line.  The closure of the set is [0,1], the closed 
> interval on 0, 1.  The boundary would be the points 0 and 1.
>
>  
>
> Mike Matsko
>
>
> ----- Original Message -----
> From: "Nick Rudnick" <joerg.rudnick at t-online.de>
> To: "Gregg Reynolds" <dev at mobileink.com>
> Cc: "Haskell Café List" <haskell-cafe at haskell.org>
> Sent: Thursday, February 18, 2010 1:55:31 PM GMT -05:00 US/Canada Eastern
> Subject: Re: [Haskell-cafe] Category Theory woes
>
> Gregg Reynolds wrote:
>
>     On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick
>     <joerg.rudnick at t-online.de <mailto:joerg.rudnick at t-online.de>> wrote:
>
>         IM(H??)O, a really introductive book on category theory still
>         is to be written -- if category theory is really that
>         fundamental (what I believe, due to its lifting of
>         restrictions usually implicit at 'orthodox maths'), than it
>         should find a reflection in our every day's common sense,
>         shouldn't it?
>
>
>     Goldblatt works for me.
>
> Accidentially, I have Goldblatt here, although I didn't read it before 
> -- you agree with me it's far away from every day's common sense, even 
> for a hobby coder?? I mean, this is not «Head first categories», is 
> it? ;-)) With «every day's common sense» I did not mean «a 
> mathematician's every day's common sense», but that of, e.g., a 
> housewife or a child...
>
> But I have became curious now for Goldblatt...
>
>      
>
>
>         * the definition of open/closed sets in topology with the
>         boundary elements of a closed set to considerable extent
>         regardable as facing to an «outside» (so that reversing these
>         terms could even appear more intuitive, or «bordered» instead
>         of closed and «unbordered» instead of open),
>
>
>     Both have a border, just in different places.
>
> Which elements form the border of an open set??
>
>
>
>         As an example, let's play a little:
>
>         Arrows: Arrows are more fundamental than objects, in fact,
>         categories may be defined with arrows only. Although I like
>         the term arrow (more than 'morphism'), I intuitively would
>         find the term «reference» less contradictive with the actual
>         intention, as this term
>
>     Arrows don't refer. 
>
> A *referrer* (object) refers to a *referee* (object) by a *reference* 
> (arrow).
>
>      
>
>         Categories: In every day's language, a category is a
>         completely different thing, without the least
>
>
>     Not necesssarily (for Kantians, Aristoteleans?)
>
> Are you sure...?? See 
> http://en.wikipedia.org/wiki/Categories_(Aristotle) ...
>
>       If memory serves, MacLane says somewhere that he and Eilenberg
>     picked the term "category" as an explicit play on the same term in
>     philosophy.
>
>     In general I find mathematical terminology well-chosen and
>     revealing, if one takes the trouble to do a little digging.  If
>     you want to know what terminological chaos really looks like try
>     linguistics.
>
> ;-) For linguistics, granted... In regard of «a little digging», don't 
> you think terminology work takes a great share, especially at 
> interdisciplinary efforts? Wouldn't it be great to be able to drop, 
> say 20% or even more, of such efforts and be able to progress more 
> fluidly ?
>
>
>     -g
>
>
>
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