Mail Archives: djgpp/2002/07/14/01:54:32
Dan Luecking <luecking AT uark DOT edu> wrote:
: On Sat, 13 Jul 2002 15:42:58 +0200, "deckerben" <deckerben AT freenet DOT de>
: wrote:
:>
:>"Martin Str|mberg" <ams AT speedy DOT ludd DOT luth DOT se> wrote in message
:>news:1026566850 DOT 605764 AT queeg DOT ludd DOT luth DOT se...
:>> Richard Dawe <rich AT phekda DOT freeserve DOT co DOT uk> wrote:
:>
:>> y = 9/5*x + 32 (or some variation thereof) surely looks extremely
:>> linear to me.
:>
:>Could it be that the term 'nonlinear' is being loosely applied here to
:>conversions requiring monomial/polynomial funcions as opposed to a simple
:>ratio of conversion?
: *Informally*, the function 1.8*x + 32 can be called linear because
: its graph is a line. *Technically*, it is an _affine_ function.
: Linear functions satisfy f(a*u + b*v) = a*f(u) + b*f(v). Affine
: functions are linear functions composed with a shift. A linear
: function might represent conversion of temperature differences,
: while an affine function would represent conversion of absolute
: temperatures.
You are completely right.
1. Lienar functionns do (mathematically) obsevere that property. (Deep
digging in high school (or college, I'm unsure which level would be
equvialent) defininitions affirms this),
2, I surely wouldn't want the matematically definition of linear
functions be diluted.
3. Nevertheless y(x)=a*x+b _is_ a linear function, isn't it.
3a. Yes. We seem to have a confusion of terms. y is an affinite
function., not a linear one. !Panic!
3b. No. y(x)=a*(x)+b is a linear function, but only to the
mathematically unexperinced. y(x)=a*x is a linear function, while
y(x)=a*x+b isn't as long as b!=0.
Further mystery (to 3a):
Why are y(x)=a*x+b, b=!0, even though of as linear funtions? They are
a straight line, which sort of supports the idea of a linear
function.
Right,
MartinS
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