Date: Jun 19, 2014 3:59 AM
Subject: Re: 1.39 - What exactly is the Mean value Theorem?
In article <firstname.lastname@example.org>,
John Gabriel <email@example.com> wrote:
> In mainstream mythmatics, the MVT is ignorantly defined as follows:
> If f is a differentiable function on (a,b), then there is at least one point
> c, such that a secant line with endpoints (a,f(a)) and (b,f(b)) is parallel
> to the tangent line at c.
> But the converse of this is NOT true in mainstream calculus:
> If f is a differentiable function on (a,b), and a tangent line exists at c,
> then a parallel secant line exists with endpoints (a,f(a)) and (b,f(b)).
> However, the MVT works regardless of the converse being true. The reason for
> this, is that ignorant baboons (that would be you) do not know its real
> meaning. In the New Calculus, the MVT is defined properly:
In JG's improper NC, nothing is defined properly for proper calculus.