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  1. Path: sparky!uunet!cs.utexas.edu!swrinde!sdd.hp.com!ux1.cso.uiuc.edu!usenet.ucs.indiana.edu!master.cs.rose-hulman.edu!master.cs.rose-hulman.edu!news
  2. From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
  3. Newsgroups: sci.math
  4. Subject: '-' operation
  5. Date: 15 Dec 1992 23:39:17 GMT
  6. Organization: Computer Science Department at Rose-Hulman
  7. Lines: 19
  8. Message-ID: <1glqb5INN6eo@master.cs.rose-hulman.edu>
  9. References: <92350.145501B7D@psuvm.psu.edu>
  10. Reply-To: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
  11. NNTP-Posting-Host: g210b-1.nextwork.rose-hulman.edu
  12.  
  13. In article <92350.145501B7D@psuvm.psu.edu> <B7D@psuvm.psu.edu> writes:
  14. > Recently my daughter brought back Problem Set II of Wisconsin Mathematics
  15. > Science and Engineering Talent Search, and Question 4 in it is as following:
  16. >          Operation @ satisfies the conditions that
  17. >                 X @ (Y @ Z) = X @ Y + Z and X @ X = 0 for any real numbers
  18. >           X, Y, Z. Show that @ must be subtraction.
  19. >For the above question, is only
  20. >thing I have to prove is X @ 0 = X?, which is not very difficult because
  21. >X @ 0 = X @ (X @ X) = X @ X + X = 0 + X = X.
  22. >I just like to know what you
  23. >  have to do to say some operation MUST be one of the basic operations.
  24.  
  25. You would need to show that X @ Y = X - Y for all X and Y.  Given what you  
  26. already have, simply let Z=Y in the first equation to discover
  27. X=X@0=X@(Y@Y)=X@Y+Y which implies X-Y=X@Y.
  28. --
  29. Bradley W. Brock, Department of Mathematics
  30. Rose-Hulman Institute of Technology  | "Resist not evil.... Love your
  31. brock@nextwork.rose-hulman.edu       |  enemies."--Jesus of Nazareth
  32.