On Sunday, October 13, 2013 8:13:49 AM UTC-5, Hetware wrote: > On 10/13/2013 1:18 AM, Arturo Magidin wrote: > > > On Saturday, October 12, 2013 7:47:12 PM UTC-5, Hetware wrote: > > >> On 10/8/2013 12:43 AM, Arturo Magidin wrote: > > >> > > >>> On Monday, October 7, 2013 7:52:32 PM UTC-5, Hetware wrote: > > >> > > >> > > >> > > >>>> Too late, I already have. I now realize I was asserting my > > >> > > >>>> assumptions > > >> > > >>>> > > >> > > >>>> in the wrong order. > > >> > > >>> > > >> > > >>> It wasn't a problem of order. The problem was that you were > > >>> asserting > > >> > > >>> assumptions without warrant. > > >> > > >>> > > >> > > >> > > >> > > >> I can assert a function to be continuous, > > > > > > You can assert anything you want, true. It doesn't stop you from > > > being wrong for "asserting" what you should not be asserting without > > > warrant. > > > > > > In particular, functions are not "declared" to be continuous, they > > > are not "assumed" to be continuous, and they are not "asserted" to be > > > continuous. > > > > That's nonsense. In variational calculus we assert the existence of an > > infinite number of continuous, twice differentiable functions which > > coincide at the boundaries of the parameter domain, but are otherwise > > arbitrary.
In variational calculus, you PROVE THE EXISTENCEE of such function; you don't take a function, dub it with a sword, and say "I declare thee to be continuous everywhere."
You were given a *specific* function, defined via a formula that does not hold everywhere. You don't get to then say "I declare this function to be continuous" without warrant.
And that's the point that we have attempted to make to you and you refuse to listen.
