On 10/19/2013 1:15 PM, Peter Percival wrote: > 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... > > and > > Let f be defined by <some formula written here> and > f is continuous because I say so. > > ?