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cite="mid:CAA5dAfo7tvJxyfArZEp_P+zJ_OpBjWz=gdmzL_fLd7-26xb-hQ@mail.gmail.com">
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<div dir="ltr" class="gmail_attr">>does a tangent of a
tangent (of a tangent) imply higher and higher derivatives,<br>
>it seems like it is precisely that?! but in what
dimension?<br>
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<div class="gmail_attr">Given a differential function R ->
R a new function can be constructed which at each point is
the derivative of the original function.</div>
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<div class="gmail_attr">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.</div>
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<div class="gmail_attr">That probably doesn't help much.</div>
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<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><br>
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