Difference between revisions of "Talk:Divisor"

Latest revision as of 23:32, 4 June 2008

Note on Edit: I changed the notation of the formula for the number of divisors, so people wouldn't be confused by the usage of the letter $n$ in both sides of the equation.

Please put four tides at the end of your message, like this: -- ~~~~. Also, what is $O(n)$ ? -- 1=2 13:01, 3 June 2008 (UTC)

Sorry about that, hehe. Oh, and I believe that is Landau notation. See this thread and the entry in MathWorld (I did not write the formula, by the way :P). To quote Merryfield:

“As $x \rightarrow ?$ , $f(x) = O(g(x))$ iff $\exists C$ such that eventually $|f(x)| \leq C|g(x)|$ .”

Basically, $O|g|$ is the upper bound of $|f|$ as $x$ approaches some value; if $f(x) = 3x^{2} + 5$ , for example, then $f(x) = O(x^{2})$ , because the term $x^2$ ‘grows’ faster than any other term that defines the function (note that this is not an equation; this is merely saying that there is some positive multiple of $|x^2|$ — say, $C|x^{2}|$ — that will always be greater than or equal to the absolute value of the function as $x$ approaches a certain value). Of course, this is a very basic definition of the big-O notation, and may not be so accurate.

-- Metafor 04:32, 5 June 2008 (UTC)

@@ Line 1: / Line 1: @@
 Note on Edit: I changed the notation of the formula for the number of divisors, so people wouldn't be confused by the usage of the letter <math>n</math> in both sides of the equation.
+Please put four tides at the end of your message, like this: <nowiki>-- ~~~~</nowiki>. Also, what is <math>O(n)</math>? -- [[User:1=2|1=2]] 13:01, 3 June 2008 (UTC)
+Sorry about that, hehe. Oh, and I believe that is Landau notation. See  [http://www.mathlinks.ro/Forum/viewtopic.php?t=31517 this thread] and the [http://mathworld.wolfram.com/LandauSymbols.html entry] in MathWorld (I did not write the formula, by the way :P). To quote Merryfield:
+“As <math>x \rightarrow ?</math>, <math>f(x) = O(g(x))</math> iff <math>\exists C</math> such that eventually <math>|f(x)| \leq C|g(x)|</math>.”
+Basically, <math>O|g|</math> is the upper bound of <math>|f|</math> as <math>x</math> approaches some value; if <math>f(x) = 3x^{2} + 5</math>, for example, then <math>f(x) = O(x^{2})</math>, because the term <math>x^2</math> ‘grows’ faster than any other term that defines the function (note that this is not an equation; this is merely saying that there is some positive multiple of <math>|x^2|</math> — say, <math>C|x^{2}|</math> — that will always be greater than or equal to the absolute value of the function as <math>x</math> approaches a certain value). Of course, this is a very basic definition of the big-O notation, and may not be so accurate.
+-- [[User:Metafor|Metafor]] 04:32, 5 June 2008 (UTC)

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Difference between revisions of "Talk:Divisor"

Latest revision as of 23:32, 4 June 2008