Re: [Phys-l] continuous but not differentiable

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2012, Mar 30, , at 09:47, John Denker wrote:

> On 03/30/2012 08:59 AM, Bernard Cleyet wrote:
> > every thing is linear in a narrow range unless poorly behaved (discontinuous).
>
> I hope this doesn't seem unduly nitpicky ... but "discontinuous" 
> functions are not the only ones that fail to have a linear 
> approximation.
>
> As a familiar example, the absolute value function is 
> continuous at the origin, but has no linear approximation 
> there, as is obvious from the fact that it is not 
> differentiable.
>
> This point is not some irrelevant mathematical nitpick.
> Functions that have no Taylor-series expansion show up in 
> physics, for example in connection with critical phenomena.
>  http://www.nobelprize.org/nobel_prizes/physics/laureates/1982/
>
> Continuing down that road, the Weierstrass function is 
> everywhere continuous but nowhere differentiable!
> _______________________________________________

list junk cut


I shoulda emphasized poorly behaved and that discontinuous as an example only.

Really,  I was aware of the differentiability requirement.

bc being overly defensive