@@Ray25689 sometimes in textbooks they don't tell you this connection, so it doesn't seem like an intuitive result. So some people could know about the lemma, but don't know it's just Newton's method.
Which is also "formally" equivalent to the implicit function theorem. I haven't seen anything deep said about these interpretations though, perhaps they help some people gain some intuition. Personally, I tend to think of each of these results on their own terms.
yee
I always like pointing out that Hensel's lemma is just the analogue of Newton's method for Qp.
You mean the proof?
@@Ray25689 sometimes in textbooks they don't tell you this connection, so it doesn't seem like an intuitive result. So some people could know about the lemma, but don't know it's just Newton's method.
@@f5673-t1h thats true
If you first read it, it looks way more abstract than it actually is, IMO
Depends on the formulation tho
Which is also "formally" equivalent to the implicit function theorem. I haven't seen anything deep said about these interpretations though, perhaps they help some people gain some intuition. Personally, I tend to think of each of these results on their own terms.
Here's a neat discussions on MSE: math.stackexchange.com/questions/48419/hensels-lemma-and-implicit-function-theorem