On Sunday, October 20, 2013 11:43:15 AM UTC-5, Hetware wrote: > On 10/19/2013 11:30 PM, Arturo Magidin wrote: > > > On Saturday, October 19, 2013 7:42:48 PM UTC-5, Hetware wrote: > > > > >> > > >>> Hey, Mr. Pot. Have you met Ms Kettle? > > > > Are those your parents?
Oh, you must think you are quite the wit. You are only half right, you know.
> You are wrong to think that I am somehow emotionally attached to being > > right in my original assertions. As I have already stated, I do not > > conform my understanding to the assertions of others unless I understand > > and can validate those assertions.
You are emotionally attached to the proposition that you are engaging in a quest for truth and understanding. You are in fact in a quest to justify yourself, as is apparent to everyone but yourself.
> > If I fully understood the subtleties involved, I would not be spending > > nearly as much time discussing this matter. I am seeking understanding, > > not vindication.
You were given all the information you needed to achieve understanding. You rejected it and instead engaged in fatuous self-aggrandizing.
> >> What convention is that? > > > > > > As I explained eariler: > > > > > > The convention that when the domain of a function is not explicitly > > > stated, then the domain is taken to be the "natural domain" of the > > > function. > > > > > > The "natural domain" of a function that is given via a formula *and > > > no other specification* is taken to be the set of all real numbers > > > for which the formula, as given, makes sense and yields a real > > > number. > > > > Given some real-valued function of real-valued arguments, defined > > everywhere on R, is it true that the function is either continuous, or > > not continuous?
Non sequitur. I gave you the convention. Are you going to continue to ignore it so you can continue to proclaim your own virtuosity in your search for "truth"?
As to your question: yes, but irrelevant. The question is: **how** are you "given a function"?
> Let P(f) be the proposition that f(x) is continuous for all x in R. > > Then !P(f) means f(x) is discontinuous for some x in R.
More irrelevant dancing. Why must you go to such lengths to remain ignorant?
> > You keep talking about assumptions of continuity, assumptions of > > > this, assumptions of that, authors trying to "bait" you, etc. But you > > > keep ignoring the conventions.
Want to keep ignoring them? Fine. But stop trying to pretend that you are searching for understanding. You are just wasting your time and working really really hard at being an ignoramus who knows big words.