Re: ICT Comments

• From: acfraud <no_reply_at_yahoogroups.com>
• Date: Sat, 12 Apr 2003 16:19:31 -0000
• Message-ID: <b79eaj+10iro_at_...>

--- In quizbowl_at_yahoogroups.com, Alexander Richman <arichman_at_b...>
wrote:
> 
> Ok, I wasn't there, and I haven't seen the question, but from my
point of 
> view, this comment is ridiculous.  Acfraud is lambasting NAQT for
starting 
> a question with a clue which the experts will know quickly while
other 
> people will still have a chance later by putting it in (sometimes
advanced) 
> calculus terms or in more basic terms at the end.  Of course, the 
> "inverse-image" definition is the most general one, but very few
people 
> meet it before their senior year as math majors, or even in grad 
> school.  I, for one, much prefer this to something with vague
similies or 
> ambiguous characterizations at the start, which happens much more
frequently.
> 
> Alex

Experts? Senior year as math majors? That's an exaggeration. It's not
even as if you need to have taken a course in point-set topology to
have seen this definition; one should at least see it in a real
analysis class. I'm pretty sure we had that definition within the
first week of the first math course I took as an undergraduate. I
expect that even a good *calculus* course, say using Spivak's text,
might mention this definition at some point.

Even if you think only "experts" could answer the question at this
point (if so, there were a large number of "experts" at the ICT!),
that clue is inexcusable in the first line of the tossup. The point
is, starting a math question with a straightforward definition is
*always* a bad idea. Even if we allow that an epsilon-delta definition
of continuous, or a definition that says "the limit exists  and equals
the value of the function," would be answerable by more people and
could be a giveaway clue, the usual definition should appear
immediately before that. I think that what I said before bears
repeating: in mathematics, you must know the definition of a term to
do anything with it. This makes definitions inherently giveaways for
anyone who knows the subject. For almost any askable math term, the
definition should be the giveaway, because it is the one thing that
must be known by anyone who uses the term in doing mathematics.
Granted, there may be rare occasions where an anecdote is better known
than the actual definition (extending "definition" to the case
"statement of a theorem", Fermat's Last Theorem provides an example.)
But what clue for "continuous" could possibly be better known than the
definition? If you state a less general definition as the giveaway,
this still doesn't excuse putting the general definition first.