← Back to context Comment by godelski 6 days ago |x| is piece wise continuous, not absolutely continuous 3 comments godelski Reply 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. :-) godelski 5 days ago 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. sfpotter 5 days ago 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.
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. :-) godelski 5 days ago 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. sfpotter 5 days ago 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.
godelski 5 days ago 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. sfpotter 5 days ago 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.
sfpotter 5 days ago 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.
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?
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.