Talk:Piecewise linear function

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Definition of a linear function[edit]

A linear function f(x) is said to be linear if and only if f(αx1+βx2) = αf(x1) + βf(x2)

According to this definition, the function f(x) = aIx + bI in the article is not linear. Joao 16:51, 1 March 2007 (UTC)

True, but nonetheless the nomenclature here is standard when used in this context. Michael Hardy 23:04, 1 March 2007 (UTC)
To be precise about "in this context": It is very common to use "linear" and "affine linear" interchangeably. It is really only in the context of linear algebra (and more generally, module theory) that these terms are strictly distinguished, and in this special case, affine linear is of no interest. In the context where the domain is not an algebraic structure, nominally a group, no one cares. (talk) 05:39, 19 March 2010 (UTC)
A definition isn't the same as an example. The example is fine for an intro, but there needs to be a section discussing measure 0 sets or simplicial complexes. What exactly is "piecewise?" From Bing's book it requires a triangulation. I.e., locally finite simplices on which the function is affine linear. (talk) 04:52, 5 October 2010 (UTC)