commutative.html

来自「数据结构词典（英文）」· HTML 代码 · 共 48 行

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<TITLE>commutative</TITLE>
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  content="Definition of commutative,
	possibly with links to more information and implementations.">
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<H1>commutative</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
A function where f(A, B) = f(B, A).
<P><strong>See also</strong>
<a href="associative.html" tppabs="http://hissa.nist.gov/dads/HTML/associative.html"><em>associative</em></a>.
<P><em>Note:
Multiplication is associative, e.g., 2  &times; (3  &times; 4) =  (2  &times; 3)  &times; 4, and commutative, e.g., 2  &times; 3 = 3  &times; 2. Subtraction is neither associative, e.g., 2 - (3 - 4)  <img src="neq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/neq.gif" border=0 height=10 width=10 alt="not equal to"> (2 - 3) - 4, nor commutative, e.g., 2 - 3  <img src="neq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/neq.gif" border=0 height=10 width=10 alt="not equal to"> 3 - 2.  Because of rounding floating point addition on a computer is not associative, e.g., (1000000 + .00001) + .00001  <img src="neq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/neq.gif" border=0 height=10 width=10 alt="not equal to"> 1000000 + (.00001 + .00001) (actual values depend on the details of the computer addition), but is commutative, e.g., 1000000 + .00001 = .00001 + 1000000.  <br> Cartesian product is associative, e.g., {1, 2}  &times; ({a, b}  &times; {X, Y}) = ({1, 2}  &times; {a, b})  &times; {X, Y}, but is not commutative, e.g., {1, 2}  &times; {a, b}  <img src="neq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/neq.gif" border=0 height=10 width=10 alt="not equal to"> {a, b}  &times; {1, 2}.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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<p>
Entry modified Wed Dec 29 12:19:10 1999.<BR>
HTML page formatted Wed Dec 29 12:19:45 1999.

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