>does a tangent of a tangent (of a tangent) imply higher and higher
derivatives,
>it seems like it is precisely that?! but in what dimension?
Given a differential function R -> R a new function can be
constructed which at each point is the derivative of the original
function.
if the original funcion is infinitely differentiable (snooth) its
derivative also is. Many funcatons such as ax + b yield a constant
function after one derivatie and infinitely many 0 functions after
that where 0 means the function f(x) = 0 for all x. Other
differentiable functions such as exp(x) or sin(x) simply return
similar infinitely differentiable functions; or themselves. A
function f: R^n -> R^m gemeralize these ideas. As for dimensions,
read about differentials, exterior derivatives, 1-forms etc.
That probably doesn't help much.
<tangent>only if the topic we are studying is infinitely differentiable
I suppose. So the implication of every tangent on a tangent is that
the topic of interest is (yet more) smooth?</tangent>-. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .
FRIAM Applied Complexity Group listserv
Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom
https://bit.ly/virtualfriam
to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
FRIAM-COMIC http://friam-comic.blogspot.com/
archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/
1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
