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== Definition of a linear function ==
A linear function ''f''(''x'') is said to be [[Linear_map|linear]] if and only if ''f''(''αx<sub>1</
According to this definition, the function ''f''(''x'') = ''a<sub>I</
: True, but nonetheless the nomenclature here is standard when used in this context. [[User:Michael Hardy|Michael Hardy]] 23:04, 1 March 2007 (UTC)
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:: 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. [[Special:Contributions/129.107.225.4|129.107.225.4]] ([[User talk:129.107.225.4|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.[[Special:Contributions/67.255.14.227|67.255.14.227]] ([[User talk:67.255.14.227|talk]]) 04:52, 5 October 2010 (UTC)
: I agree with the OP and I also think it should be stated somewhere that this name "piecewise linear" means that the function is piecewise affine, not linear (even if you call that "piecewise linear" and you define "piecewise linear" to be that). Yes, the current definition '''''implies''''' that it is piecewise affine, and that this is called "piecewise linear", but
:* it is '''not''' said (and should be said) that this means that the function is *piecewise affine*
:* it is '''not''' said (and should be said) that the function is (a priori) *nowhere* a linear function (not even piecewise, i.e., on some subinterval), and none of the affine functions to which it may be equal on some interval, is linear in the sense of the definition [need it to be said? is there another sense?] of what means for a function to be linear. — [[User:MFH|MFH]]:[[User talk:MFH|Talk]] 23:38, 1 December 2022 (UTC)
:PS: I have just created the redirect [[Piecewise affine function]]. At least that... 15 years later...
== Square wave ==
The square wave is not a function, thus I will be removing it. It fails the vertical-line test, which is when you pass a vertical line through the graph of a function, the line only crosses one point.
Still unsure about the sawtooth function.
--[[User:SaveTheWild|SaveTheWild]] ([[User talk:SaveTheWild|talk]]) 00:39, 12 November 2019 (UTC)
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