zlacker

|x| is piece wise continuous, not absolutely continuous

>>godels+(OP)
For a function to be locally linear at a point, it needs to be differentiable at that point... |x| isn't differentiable at 0, so it isn't locally linear at 0... that's the entirety of what I'm saying. :-)

>>sfpott+KX1
You're not wrong. But it has nothing to do with what I said. I think you missed an important word...

Btw, my point was all about how nuances make things hard. So ironically, thanks for making my point clearer.

>>godels+FB2
Nothing to do with what you said?

  This is true for any curve...

  If your curve is continuous, it is locally linear.

Hmm...

Sometimes naive approximations are all you've got; and in fact, aren't naive at all. They're just basic. Don't overthink it.