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Comment by sfpotter

5 days ago

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. :-)

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.

  • 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.