Talk:Level set/Archive 1

Archive 1

Bold f

f is inconsistently bold (suggesting a vector) or not bold. I suppose we are talking about a scalar here; then it should not be bold.--Patrick 22:37, 12 May 2004 (UTC)

sorry bout that (hopefully fixed now) Dysprosia 22:59, 12 May 2004 (UTC)

Level set vs fiber (or fibre)

Level sets are simply the inverse images of singletons, more usually called "fibers" (or "fibres"). I think this connection should be made somewhere in this article. Is the term "level set" restricted to just real-valued functions of n variables? Or is it really just a synonym for "fiber"? PlanetMath seems to think so:. On the other hand, Mathworld's definition is even more restrictive, requiring "f" to be a differentiable function f : Rⁿ → R. — Paul August ☎ 19:02, August 7, 2005 (UTC)

Patrick has now added: "A level set is also called a fiber." Paul August ☎ 15:10, August 8, 2005 (UTC)

Yes, this seems correct. Dysprosia 04:48, 9 August 2005 (UTC)

Level set may be larger than a hypersurface

It should be pointed out that the level set is not always a curve or a hypersurface (for exampe if f is constant on an open set).--Pokipsy76 11:12, 27 October 2005 (UTC)

Anyone notice that "Implicit surface," listed in the Links section, leads back to this entry via a redirect? — Preceding unsigned comment added by 68.218.225.169 (talk) 18:30, 18 June 2007 (UTC)

Thanks, I removed that self-redirect. Oleg Alexandrov (talk) 02:10, 19 June 2007 (UTC)

n or x_n?

• Current: A level hypersurface is the set of all real-valued roots of an equation in x_n (n > 3) variables.
• Proposal: A level hypersurface is the set of all real-valued roots of an equation in n (n > 3) variables.

? --Abdull (talk) 21:20, 2 July 2008 (UTC)

I agree. I fixed that. Oleg Alexandrov (talk) 03:59, 3 July 2008 (UTC)

"proof"

The "proof" that the gradient of a function is normal to its level set needs work. Using three lines and writing everything in shorthand (vector form) for an audience that looks at the page (assumedly) not knowing what a level set even is, and then using math at a higher level than can be reasonably expected from someone who doesn't know what a level set is (i.e., jacobians and vector-valued functions), is just silly. feel free to bother me on my talk page if you reply here and i don't respond. Charibdis (talk) 04:36, 18 February 2010 (UTC)

maybe I should clarify that I'm assuming the first time someone might see a level set is in undergraduate multivariable calc. Charibdis (talk) 06:06, 12 April 2010 (UTC)