Talk:Sign function

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I removed the following

Also, if the step function h0(x) is thought of as a mathematical switch, with h0(x) = 0, then the signum function can be expressed as
\sgn x = h_0 (|x|) (-1)^{h_0(-x)}.

as I do not understand what it adds.--Henrygb 14:34, 29 Mar 2005 (UTC)

Since h(x) can be different things, it looks like someone was just leaving a note of how to calculate sgn for people who are used to using another definition of h(x)? Who added it in the first place? - Omegatron 16:12, Mar 29, 2005 (UTC)

isn't it kinda dumb to have this and the signum function page, which are talking about the same thing????Scythe33

Contents

[edit] Link to "sign" page

In the first paragraph, the word "sign" in "extracts the sign of a real number" was linked to the Negative and non-negative numbers page. There doesn't seem to be a page for the correct concept. I have removed the link. Iggle 08:27, 27 March 2006 (UTC)

[edit] Pronunciation?

Does anyone know the correct pronunciation of "signum"? I'd intuitively say "sigg-numb", but in context, "sigh-numb" might also be correct. Might be worth putting in.


Hmmmmm... I checked Wiktionary, but it didn't provide a pronunciation. And dictionary.com provided no entries. I usually pronounce it "sigg-numb," like you. -- He Who Is[ Talk ] 18:17, 22 June 2006 (UTC)

Since it is (presumably) Latin, the "g" should be pronounced. Zaslav (talk) 01:09, 27 February 2008 (UTC)
"Signum" pronounces as "SIN-yoom". How to Pronounce Latin --Octra Bond (talk) 05:48, 8 June 2008 (UTC)
The pronunciation given at that site is the pronunciation of Ecclesiastical Latin, as is made quite clear there. If the word signum is pronounced as part of Latin liturgy, for instance when reading in the liturgy of Christmas from the Gospel of Luke 2:12 Et hoc vobis signum : invenietis infantem pannis involutum, et positum in præsepio, you can expect to hear "SEEN-yoom" (or, if the speaker is Italian, "SEEN-yoom-uh"). In Classical Latin, as far as we know, the 'g' was hard, as in "SEEGG-noom". In addressing an English-speaking audience, I'd go with "SIGG-numb", as if the word has become an accepted English word, in analogy to how the 'g' is pronounced in 'magnificent' and 'recognition'.  --Lambiam 19:22, 8 June 2008 (UTC)

[edit] Complex Signum

I've added a section on the signum of complex numbers. Feel free to critique or remove, if you feel it is extrenuous. -- He Who Is[ Talk ] 18:14, 22 June 2006 (UTC)

  • I've just added a description of csgn from Maple, which is another generalization of signum to complex numbers. I think it was neccessary because csgn redirects here but there is no mention of csgn. Rjgodoy 02:44, 30 May 2007 (UTC)

[edit] Signature Function (permutations)?

Sgn redirects here, but there's no mention of the signature of a permutation matrix which is also denoted with the sgn() function. That's actually what I was trying to find, and only happened to stumble across it linked from another article. 142.59.195.50 19:36, 31 March 2007 (UTC)

  • Hello, and thanks for the comment. I have added a note about sgn(σ) that suggest Levi-Civita symbol. The generalization to n dimensions of Levi-Civita pseudotensor is another form for the sgn(σ) function you refer. Rjgodoy 02:29, 30 May 2007 (UTC)

[edit] Generalized signum function

The first paragraph of this section says "~\varepsilon(x)^2 =1~ everywhere, including at the point ~x=0~" but the second says "~\varepsilon(x)~ cannot be evaluated at ~x=0~". Why does it conflict itself? --Octra Bond (talk) 05:55, 8 June 2008 (UTC)

Generalized functions do not behave like ordinary functions. The paragraph pertains to a construction in the algebra of generalized functions developed by Yu. M. Shirokov; see Wikisource:Algebra of generalized functions (Shirokov). In that algebra, δ(x)2 = 0 at x = 0 even though δ(0) = +infinity. The notation is (in my opinion) misleading, since what is being multiplied are the generalized functions themselves, and a notationally clearer statement would have been that (ε★ε)(x) = 1 and (δ★δ)(x) = 0 for all x, in which ★ denotes the (non-commutative) operation of multiplication for generalized functions.  --Lambiam 18:40, 8 June 2008 (UTC)