Talk:Idempotence
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> Elevator call buttons are idempotent, though many people think they are not.
That cracked me up!
[edit] Pronunciation?
Is there a correct pronunciation for idempotent? Is it like omnipotent (om-nip-o-tent), so id-EMP-o-tent, or is it more like the two seperate words idem + potent
- I'd say EYE-dm-POT-nt, but then I speak Brit. Charles Matthews 07:57, 30 Jun 2004 (UTC)
- Ditto, but then I speak Australian ;) Dysprosia 08:01, 30 Jun 2004 (UTC)
- Actually the British is more like EYE-dm-PO-tnt, I guess. Charles Matthews
- I'd just like to pedantically point out that it would be pronounced i-DEM-po-tent because because syllable onsets are maximized. daesotho 20:33, 21 Oct 2004 (UTC)
The opening sentence is
- "In mathematics, an idempotent element (IPA [ˈaɪdɛmˌpotnt/, like eye-dem-potent) is an element which, intuitively, leaves something unchanged. "
I'd say this is quite misleading because when we're thinking of idempotents as operating on something, they don't in general leave it unchanged, they just don't change it any more when you apply them again. A better version in my opinion would be
- "In mathematics an idempotent is, intuitvely, something which changes something, but when applied again to the changed version of that thing does not change it any further."
And by the way I think it's silly giving a pronounciation guide as this is just imposing a particular accent. (For what it's worth I pronounce idempotent with a short 'i', as in the word 'id'). Alex Selby
- JA: I think this is an idyll question. Jon Awbrey 14:16, 14 February 2006 (UTC)
[edit] There is only one meaning given here
The article starts by claiming that there are two meanings, but clearly they are the same. The "unary operation" definition is the same because the operation involved is function composition which is a binary operation. If @ denotes function composition, then an idempotent function f is one satisfying f@f=f. This is in fact suggested in the parenthetical comment "(or for a function, composed with)" near the start, but then the article continues as if functions are special. They aren't. McKay 10:52, 29 June 2006 (UTC)
[edit] Primitive Idempotents
Primitive idempotents are important in quantum mechanics as they are the pure states in density matrix or density operator theory. The pure states can be reprsented by spinors, for example if |a> is a spinor, then |a><a| is a primitive idempotent. See the "Density Matrix Formalism" portion of Frank Porter's quantum mechanics class notes (Cal Tech): http://www.cithep.caltech.edu/~fcp/physics/quantumMechanics/
Can we add this to the discussion? What other examples of idempotents are important in physics and mathematics? If this is something that should be included, let me know or do it yourself.
CarlAB 02:57, 7 October 2006 (UTC)
