LL-L "Lexicon" 2005.09.14 (03) [E]

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From: Sandy Fleming <sandy at scotstext.org>
Subject: "Lexicon" [E]

> Please have a look at de.wikipedia.org/wiki/Gruppentheorie
>
> That page also has a short introduction for "Nichtmathematiker".
>
> "Groups" are special "set"s with special properties. You take a set (of
> elements) and you define two operations on this set. And once you have
> checked (mathematically spoken "proved") that these two operations work 
> well
> on this set, you have a "group". And then you have come very far, because
> you can study groups in general and then you know that all the properties 
> of
> groups then apply to your set. Then you can even find lots and lots of 
> very
> special groups like "Abel'sche Gruppe" and all those other groups that you
> can find on de.wikipedia.org/wiki/Gruppentheorie

I'm not familiar with wikipedia and this explanation doesn't give me any 
motivation to bother getting familiar with it!

A group has one operation, not two. A set with two operations that "work 
well" (as this writer so condescendingly puts it) is called a "ring".

> So a "set" is more like bottles that you place together on a shelf. Sets
> come in all flavours. Some have names, some have their own mathematical
> symbols (like the set of the integer numbers) and others just pop up,
> because you just like them or because you need them in an exercise. Let us
> just invent a group {1,2, "hallo", "Ron"} and let us name this set 
> "Heiko's
> Example". You see: a set can have objects of different types.

OK, so this is Naive Set Theory they're talking about - it figures!  :)

> So if we use _Koppel_ for _set_, what will we use for _Gruppe_?? And maybe
> the elements in a _Koppel_ would stick too close together to be a _set_??

Words like "set" and "group" would be difficult for Scots speakers to 
pronounce if we had to borrow them directly from Englishes outside of 
Scotland, since the Scots pronunciation system is so different from that of 
English.

As it happens we have our own form of English, "Scottish English", which is 
English pronounced with Scots phonemes. So Scottish English acts as a 
"linguistic adaptor" between Scots and English, and unless there is an 
obvious Scots word already we can almost always simply borrow technical 
words from English, "adapted" via Scottish English.

Sandy
http://scotstext.org/

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