Re: Sectionals questions

mac4731 <*no_reply_at_yahoogroups.com*> · Thu, 13 Feb 2003 17:09:20 -0000

I hesitate to post too much about technical mathematics theorems 
here, so feel free to ignore the rest of this, but a few things have 
been mentioned that I think are worth addressing since they've 
already been brought up. First of all, in my experience, the axiom of 
choice has come up as an answer far more often than Zorn's lemma. In 
fact, the only times I've heard Zorn come up is as a (overused) lead-
in to the axiom of choice; I can't remember Zorn ever being an answer 
in its own right (though maybe things have changed recently, and I 
just haven't played on the right question sets to see this). There's 
probably nothing wrong with this, since the axiom of choice version 
is likely the one most easily understood by the non-math crowd. 
However, as someone who is currently doing algebra research, I can 
tell you that Zorn's lemma is the version of the axoim of choice idea 
that is used almost ubiquitously in modern mathematics; I can't 
recall ever using the axiom of choice version, but I have used Zorn's 
lemma multiple times in the last week alone. I think both have their 
place in quizbowl, being a major example of an undecidable 
proposition (the same reason the continuum hypothesis comes up) and 
one of the most troublesome issues faced in modern mathematics.

Kelly

--- In quizbowl_at_yahoogroups.com, nate_1729 <no_reply_at_y...> wrote:
> I think Jordan's right here.  Given the set-theoretic underpinnings 
> of, well, just about everything, the concept of surjectivity has to 
> be one of the N most important concepts in math.
> 
> Indeed, surjectivity is an excellent example of an important 
concept 
> that is highly accessible to those without specialized training -- 
> look at various pigeon-hole arguments for examples of elementary 
and 
> elegant proofs that use only basic (and intuitive) set theory.
> 
> It's laughable to suggest that surjectivity is too specialized, 
when 
> Zorn's lemma and Russell's paradox, just to name two, are asked 
> frequently -- both of those are (when studied rigorously) 
> exponentially less accessible to the non-specialist.  (One might 
> defend these on the grounds that they're more interesting in a 
purely 
> philosophical sense -- I would disagree, but my point here is to 
note 
> that any 'accessibilty' or 'specialization' argument is without 
> basis.)
> 
> I applaud efforts to ask about surjectivity and other important and 
> accessible concepts, in mathematics and elsewhere in academia.  I 
> hope that we can eliminate the bias toward things named after 
people -
> - I believe that this at least partially accounts for the 
popularity 
> of Zorn's lemma and Russell's paradox.  Among other things, the 
fact 
> that "Zorn's lemma" comes up more than the "axiom of choice" 
[they're 
> equivalent], to me, provides rather compelling evidence for this 
> stance.  (More easily checked, lots of math answers start with 
> capital letters.)
> 
> --Nate 
>