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comments re draft version 2.0

From: David Eppstein <eppstein@ics.uci.edu>
Date: Sun, 02 Apr 2000 12:15:15 -0700
To: www-math@w3.org
Message-ID: <5144177.3163666515@cx344290-c.irvn1.occa.home.com>
These must be frequently asked questions (I have only seen the draft 
proposal, not any mailing list archives etc), but:


(1) As someone who works in analysis of algorithms, the most common 
notation I use beyond basic arithmetic is O-notation, and certainly this 
falls within your criterion of "the first two years of college" for 
computer science students.  How do you represent that in content markup 
style?  Of course one would also need o(), omega(), Omega(), and Theta(). 
One could get something resembling the correct visual appearance with 
<apply><ci>O</ci>...</apply> but this seems to violate the idea of 
representing the semantics in the markup, e.g. I note that standard 
deviation is represented with <apply><sdev/>...</apply> rather than 
<apply><ci>&sigma;</ci>...</apply>


(2) How would you represent an expression like $\lfloor (n+1)/6\rfloor$ in 
content markup style? I am guessing it should be something like 
<apply><floor/>...</apply> but there seems to be no predefined <floor/> -- 
this is important because it's a common standard function with an unusual 
visual representation.  Ditto ceiling.


(3) How does one represent chains of inequalities in content markup?  You 
list the equalities and inequalities as n-ary but what about chains that 
mix the two, e.g. (from some of my course notes)
$$T(n) = 2\sum_{i=0}^{\log n} n/2^i \log(2^i)
= 2\sum_{i=0}^{\log n} i/2^i
\le 2\sum_{i=0}^{\infty} i/2^i
= 4n$$

-- 
David Eppstein       UC Irvine Dept. of Information & Computer Science
eppstein@ics.uci.edu http://www.ics.uci.edu/~eppstein/
Received on Sunday, 2 April 2000 15:15:20 GMT

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