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 msmat...@comcast.net
To: Nick Rudnick joerg.rudn...@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.rudn...@t-online.de
To: Gregg Reynolds d...@mobileink.com
Cc: Haskell Café List haskell-cafe@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.rudn...@t-online.de mailto:joerg.rudn...@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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