Difference between revisions of "Talk:Divisor"
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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) | 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) | ||
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| + | 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: | ||
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| + | “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>.” | ||
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| + | 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. | ||
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| + | -- [[User:Metafor|Metafor]] 04:32, 5 June 2008 (UTC) | ||
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 
in both sides of the equation.
Please put four tides at the end of your message, like this: -- ~~~~. Also, what is 
? -- 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 
, 
iff 
such that eventually 
.”
Basically, 
is the upper bound of 
as 
approaches some value; if 
, for example, then 
, because the term 
‘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 
— say, 
— that will always be greater than or equal to the absolute value of the function as 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)
