← Back to context Comment by godelski 1 year ago |x| is piece wise continuous, not absolutely continuous 3 comments godelski Reply sfpotter 1 year 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 1 year 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 1 year 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 1 year 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 1 year 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 1 year 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 1 year 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 1 year 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 1 year 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.