For faster navigation, this Iframe is preloading the Wikiwand page for
分配律.
分配律(distributive property)是二元运算的一个性质,它起源于基本代数运算,同时部分抽象代数运算亦符合该定律
定义
设
及
是定义在集合
上的两个二元运算,我们说
对于
满足左分配律,如果:
;
对于
满足右分配律,如果:
;
- 如果
对于
同时满足左分配律和右分配律,那么我们说
对于
满足分配律。
如果
满足交换律,那么以上三条语句在逻辑上是等价的。
例子
- 除了实数以外,自然数、复数和基数中的乘法都对加法满足分配律。
- 实数及复数中的除法都对加法满足右分配律,但不满足左分配律。
- 序数的乘法对加法只满足左分配律,不满足右分配律。
- 矩阵乘法对矩阵加法满足分配律(但不满足交换律)。
- 集合的并集对交集满足分配律,交集对并集也满足分配律。另外,交集对对称差也满足分配律。
- 逻辑析取对逻辑合取满足分配律,逻辑合取对逻辑析取也满足分配律。另外,逻辑合取对逻辑异或也满足分配律。
- 对于实数(或任何全序集合),最大值对最小值满足分配律,反之亦然:
![{\displaystyle \operatorname {max} (a,\operatorname {min} (b,c))=\operatorname {min} (\operatorname {max} (a,b),\operatorname {max} (a,c))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e90556a3f4a9826d754c968e539c40d4a1319da6)
。
![{\displaystyle \operatorname {gcd} (a,\operatorname {lcm} (b,c))=\operatorname {lcm} (\operatorname {gcd} (a,b),\operatorname {gcd} (a,c))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a95acf648c6852eb4358edde72584bfc903a46f3)
。
- 对于实数,加法对最大值满足分配律,对最小值也满足分配律:
![{\displaystyle a+\operatorname {max} (b,c)=\operatorname {max} (a+b,a+c)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/814d7a644fd59fa0ec8ed297e9605ab4100b92dd)
。
{{bottomLinkPreText}}
{{bottomLinkText}}
This page is based on a Wikipedia article written by
contributors (read/edit).
Text is available under the
CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.
{{current.index+1}} of {{items.length}}
Thanks for reporting this video!
This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.
Please download and use one of the following browsers:
An extension you use may be preventing Wikiwand articles from loading properly.
If you're using HTTPS Everywhere or you're unable to access any article on Wikiwand, please consider switching to HTTPS (https://www.wikiwand.com).
An extension you use may be preventing Wikiwand articles from loading properly.
If you are using an Ad-Blocker, it might have mistakenly blocked our content.
You will need to temporarily disable your Ad-blocker to view this page.
✕
This article was just edited, click to reload
Please click Add in the dialog above
Please click Allow in the top-left corner,
then click Install Now in the dialog
Please click Open in the download dialog,
then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list,
then click Install
{{::$root.activation.text}}
Follow Us
Don't forget to rate us
Oh no, there's been an error
Please help us solve this error by emailing us at
support@wikiwand.com
Let us know what you've done that caused this error, what browser you're using, and whether you have any special extensions/add-ons installed.
Thank you!