April 21st, 2015, 11:11 AM  #11 
Member Joined: Jan 2014 Posts: 86 Thanks: 4 
Yet, I could just as well label i as the error number, is it imaginary or in reality an error? We can imagine both real things as well as errors. This course of thought leads me to the idea of quantifying errors.

April 21st, 2015, 11:20 AM  #12 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  No. We've learned vastly more about them in the time since De Morgan suggested that. (And frankly, he was a bit behind the times in that respect  that view was typical 300 years ago but already oldfashioned by De Morgan's day.)

April 21st, 2015, 11:24 AM  #13 
Member Joined: Jan 2014 Posts: 86 Thanks: 4 
If De Morgan was wrong then how does the mother of complex numbers, the equation x^2 = 1, reconciles with the property that 1 times 1 = 1?

April 21st, 2015, 12:59 PM  #14 
Global Moderator Joined: May 2007 Posts: 6,805 Thanks: 716  
April 21st, 2015, 07:12 PM  #15 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Well, if x^2 = y, and y^2 = z, then x is a fourth root of z. In this case i is a fourth root of unity. This shouldn't be surprising, though, given the Fundamental Theorem of Algebra.


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