non game related math question
quote:Original post by Anonymous Poster
a(x)=2-x is not linear. Any linear function has a(0)=0.
It is indeed a linear function of x, since x is not raised to any power (except to the power of 1), and the coefficient of x is a constant (coefficient = 1).
If linear functions always satisfied a(0) = 0, then all lines would pass through the origin, which clearly isn''t true.
Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.
Beware anonymous cowards who post silly mathematical comments. I speak from experience here. I was once dragged into a pointless debate in the GDNet Lounge that ended up turning into a flame war because anonymous posters tend to be good trollers. (The debate was whether or not the infinite decimal 0.9999... is equal to 1).
Good point and thanks for the advice Graylien!
Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.
Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.
Hey grhodes_at_work, I am the anonymous poster again.
Since you are a senior scientist I thought you would be smarter than to make your erroneous correction to my previous post.
A linear function is not defined as a line. A linear function, in the most common definition, is a function f:V->V, where V is a vector space, such that
f(x+y)=f(x)+f(y) for all x,y in V.
This means that f(0)=f(0+0)=f(0)+f(0), i.e. that f(0)=0.
Just because the function a(x)=2-x is not a linear function does not mean that the graph of a(x) is not a line. These are two completely different things. a(x) here is an affine function, as I said before, and the graph of all affine functions are lines.
Since you are a senior scientist I thought you would be smarter than to make your erroneous correction to my previous post.
A linear function is not defined as a line. A linear function, in the most common definition, is a function f:V->V, where V is a vector space, such that
f(x+y)=f(x)+f(y) for all x,y in V.
This means that f(0)=f(0+0)=f(0)+f(0), i.e. that f(0)=0.
Just because the function a(x)=2-x is not a linear function does not mean that the graph of a(x) is not a line. These are two completely different things. a(x) here is an affine function, as I said before, and the graph of all affine functions are lines.
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