Hetware wrote: > On 10/19/2013 7:34 AM, Peter Percival wrote: >> Hetware wrote: >> >>> If we define f(x) as >>> >>> f(x) = x/x and c[f(x)], >> >> That's cheating. You've been told at least eight million times > > In psychology that's called cognitive distortion, and is an example of > how emotions cause our thoughts to be irrational. > >> that you >> may define f with a formula, but you cannot put "and c[f(x)]" in the >> definition. If c[f(x)] is true it has to be proved _from_ the >> definition. > > Sayin' it don't make it so. > > In variational calculus we assume the existence of a continuous, twice > differentiable function over some domain and then seek a closed form > solution that satisfies the conditions given for the system.
You really see no difference between
Let f be a continuous, twice differentiable function...
Let f be defined by <some formula written here> and f is continuous because I say so.
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg