Forwarding from Math Forum: more on how I think it pays students nowadays to look at numbers differently, now that they're consistently implemented as instances of a type which includes methods and attributes per OOP. Context: http://mathforum.org/kb/message.jspa?messageID=5657989&tstart=0 Kirby ==== Re: Operations: binary vs unary Posted: Apr 19, 2007 12:38 PM In my math courses we consider a number's operational capabilities to be a part of its "type" or "class". Whereas we have the standard +, -, /, * operators to play with, it's also possible to invoke these operations using a consistent "dot notation" -- which I consider a part of contemporary mathematics (characteristic of several self-executing MNs [1]). Using Python... IDLE 1.2
3 .__neg__() # unary op takes no argument -3 -------3 -3 3 .__add__(5) 8 3 .__sub__(5) # binary op expects an argument -2
Of course this still looks strange to people who grew up in the 1900s (as I did) and think in a different paradigm. In the old way of thinking, operations were not included in our type definitions. The idea of "adding" was somehow independent of the set theory definitions (since dispensed with) of integers for example. Nowadays, a number such as the integer 1 has "guts", just as a string does.[2] Kirby Urner Saturday Academy Silicon Forest, Oregon [1] MNs = math notations, per Kenneth Iverson's treatise thereon: http://www.cacs.louisiana.edu/~mgr/404/burks/language/apl/camnweb/camn.htm [2] 'OOP Meets Algebra, Suggesting New "Ways of Looking" ' by Kirby Urner First posted: Feb 24, 1999 http://www.4dsolutions.net/ocn/oopalgebra.html