Talk:Asymptotic analysis
From Wikipedia, the free encyclopedia
Notation query: f ~ g can be written with the keyboard character ~. HTML isn't needed. For my browser this is fine.
Charles Matthews 11:15, 20 Oct 2004 (UTC)
On my current browser it looks fine, but whatever I was using before showed it up too high. I guess it is pot-luck according to the font one is using. Now I see there is a html entity: ∼ aka ∼ --Zero 11:43, 20 Oct 2004 (UTC)
To Michael's question: "Do some people prefer \ldots to \cdots between plus signs? Why?", my answers are (1) they have no artistic taste, (2) they are so old that they learned their typography on typewriters where temporarily shifting the baseline by a fraction of a line was too much trouble, (3) none of the above cos I just made them all up. ;-) -- Zero 03:59, 6 Nov 2004 (UTC)
Could somebody please include some layman's language in this article at the top; just a sentence saying that asymptotic analysis covers how long something takes to be processed, or whatever the definition is. Thanks. -- Ian Howlett 19:30, 4 Jul 2005 (UTC)
[edit] ≃
ISO 31-11 uses the Unicode character ≃ to denote "is asymptotically equal to". Is this character actually in usage? Wouldn't it then be a good addition to the this article? --Abdull 21:16, 28 May 2006 (UTC)
- I don't think there is concensus on use of several such "equivalence relation symbols" - some use ~ for asympt.equiv, some use it for proportional, some use a kind of alpha for the latter. I think this is a fashion phenomenon under constant evolution. you might compare the HTML entity code vs amstex commands for the following symbols (from http://www.acronet.net/tags/characters.html):
& sim; ∼ tilde operator = varies with = similar to = proportional = asympt.equiv. & cong; ≅ approximately equal to / (geometrically) congruent & asymp; ≈ almost equal to / asymptot.equal (\approx in latex) & equiv; ≡ identical to (used by mathematicians for (arithmetic) congruence)
- (and the symbol of this section's title is displayed as division sign in the "edit summary" line of my browser...)— MFH:Talk 22:19, 12 February 2007 (UTC)
[edit] Definition of asymptotic equivalence
Someone did not like my more general definition of asymptotic equivalence, which I took to be f=g(1+o(1)). He argued, that "my" definition (which is common in asymptotic analysis) was not more general, because asymptotic equivalence only deals with limits... Please, explain to me, by using the present definition of the article (lim f/g = 1), whether or not 0 is asymptotically equivalent to 0, and then explain to me, why my definition is not more general than the present definition. According to my definition, 0 ist asymptotically equivalent to 0. ASlateff 128.131.37.74 05:27, 11 February 2007 (UTC)
- I agree that the current definition (f ~ g iff lim f/g = 1) is not good. Among others, the function f/g may not be defined even though the function g/f is defined, so there is clearly a problem. I prefer the f = (1+o(1)) g definition. (I prefer putting it that way round because many non-specialists would get confused by the other one thinking that 1+o(1) would be an argument to g.) Else, one can also put it f-g = o(g) (which is of course the same). — MFH:Talk 15:37, 12 February 2007 (UTC)
-
- May I suggest to reestablish my version of the article? ASlateff 128.131.37.74 00:43, 17 February 2007 (UTC)
