Talk:Linearity

message: The linearity of the function f(x)=mx+c over the reals is controversial. 
: Let's get a closer look: all entities in Reals; just c may be 0...
: Superposition is not always satisfied: 
: f(y+z)=m(y+z)+c  is equal to  f(y)+f(z)=my+c+mz+c=m(y+z)+2c  iff c=0.
: Homogeneity is not always satisfied:
: af(x)=a(mx+c)=amx+ac  is equal to  f(ax)=amx+c  iff c=0.
jimmer_lactic
: I've added that that's a different usage of the term linear. I hope that helps! -- Oliver P. 22:02 5 Jun 2003 (UTC)
: As jimmer_lactic showed, the definition of linearity in the introduction is wrong, and should be removed. The definition in the intro may be correct according to common parlance but this is not a dictionary. My suggestion is to keep only the mathematical definition, and move the common parlance definition to the wiktionary. Some of the other definitions do not need to be deleted but can be moved/created as their own pages. So we have one page for linearity in math, and one for linearity in art etc.
rasmuslarsen
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Not true for all finite fields that superposition imples linearity: just for the prime fields.
Charles Matthews 06:37, 10 Oct 2003 (UTC)
thread_title: Initial comments

message: I thought linear came from "linea" (line). 62.189.34.9 20:53, 30 December 2005 (UTC)
thread_title: Linearis?

message: I've added a rating for the maths content of this page. The other content should probably be moved out and linked via Linear (disambiguation). Geometry guy 15:54, 18 May 2007 (UTC)
thread_title: Maths rating and dab

message: :Feel free to state your position on the renaming proposal by beginning a new line in this section with *Support or *Oppose, then sign your comment with ~~~~. Since polling is not a substitute for discussion, please explain your reasons, taking into account Wikipedia's policy on article titles.
*Support; article titles should be nouns where possible.  Powers T 15:17, 7 February 2012 (UTC)
thread_title: Survey

message: Specifically regarding "operating region." The page used to say(paraphrased): that as the input signal increased, distortion can be formed(true) because the system is taken out of the linear region of the transfer function (ambiguous).
I removed the second ambiguous statement because it is strictly not true. A transfer function has many definitions and many are only defined on a linear system. Saying a transfer function "is taken out of the linear region" is not clear. A nonlinear system can have input-output characteristics with linear and non-linear regions. For high input signal amplitudes the transfer characteristic can exhibit more nonlinear behavior than at low input signal amplitudes. The article does not distinguish these circumstances from traditional transfer functions defined on a linear system, making the statement as previously written ambiguous. 
Affine.function (talk) 17:50, 19 August 2020 (UTC)
thread_title:  Linearity in Electronics 

message: This article uses the symbol ⊕ for the concept denoted ∧ in the referenced article titled "Boolean algebra." Please either define terms here or change them to agree with the other article. Burressd (talk) 15:51, 23 April 2024 (UTC)
thread_title:  Boolean symbol for "and"