On Jan 9, 2009, at 8:15 AM, David Hobby wrote: > Ronn! Blankenship wrote: > ... >>> But I did know there had to be one. I think >>> these are called "affine" transformations. >>> (Linear is x --> ax, and Affine is x --> ax + b.) >> >> y = mx + b is a linear equation. (With slope m and y-intercept b.) >> >> . . . ronn! :) > > Ronn-- > > Why, yes it is. But "linear transformation" > has a different meaning. This is one of those > places where usage may differ between simple > and advanced Math. Once people got into > doing transformations to vector spaces by > matrix multiplication, they decided that they > wanted to define "T is linear" as > "T(ax + by) = a T(x) + b T(y) always holds". > Once you do that, T(0) = 0, and you don't > get to add a constant as part of a linear > transformation. > > Another place where this kind of thing shows > up is in the definition of the natural numbers. > Do they start at 0 or at 1? On a basic level, > starting at 1 makes sense. But in set theory > (or computer science) starting at 0 works better. > > The crude answer to you would be to say: > "Oh, so it means that? Then go edit Wikipedia > to say so." See: > http://en.wikipedia.org/wiki/Linear_transformation > > That's a great function of Wikipedia--standardizing > nomenclature. > > ---David
To the extent to which nomenclature can be standardized, that is. (Some terms have overlapping and somewhat incompatible definitions across the namespaces of different specialties, and sometimes all that can be done to remove the ambiguity is specify the namespace. :) And some of us became accustomed at an early age to integer number systems that wrap around from (2^n)-1 to -2^n, for various relatively small values of n. :) Overflow bit Maru _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
