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单词 Associative property
释义

Associative property

中文百科

结合律

在数学中,结合律是二元运算可以有的一个性质,意指在一个包含有二个以上的可结合运算子的表达式,只要算子的位置没有改变,其运算的顺序就不会对运算出来的值有影响。亦即,重新排列表达式中的括号并不会改变其值。例如:

上式中的括号虽然重新排列了,但表达式的值依然不变。当这在任何实数的加法上都成立时,我们说「实数的加法是一个可结合的运算」。

结合律不应该和交换律相混淆。交换律会改变表达式中算子的位置,而结合律则不会。例如:

是一个结合律的例子,因为其中的括号改变了(且因此运算子在运算中的顺序也改变了),而算子5、2、1则在原来的位置中。再来,

英语百科

Associative property 结合律

A binary operation ∗ on the set S is associative when this diagram commutes. That is, when the two paths from S×S×S to S compose to the same function from S×S×S to S.
In the absence of the associative property, five factors a, b, c, d, e result in a Tamari lattice of order four, possibly different products.

In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is, rearranging the parentheses in such an expression will not change its value. Consider the following equations:

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更新时间:2025/6/21 5:13:38