结合律

We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。

The combination rule of the method satisfies commutative law and associative law, fully uses information of conflict evidences, and solves three kinds of problems appeared in conflict evidences combination process.

该组合方法满足结合律和交换律，充分利用冲突证据信息，解决了冲突证据组合中的三类问题。

So 2/4=1/2. Here we have used the associative law or the cancellation law for multiplication, which are satisfied for natural numbers, now we assume they are satisfied with fraction numbers.

2的数，所以2/4=1/2。这里我们用到了乘法结合律也可以用消去律，本来这些运算律是对正整数乘法适用的，但对于有分数参加的乘法我们也规定适用。

In the 2nd one we have already a+(b+1)= a+b'='=+1,this is the first step of associative law for addition,further more we can verify the associative law and commutative law for addition.

而在第二条中已经有a+(b+1)= a+b'='=+1，就是加法结合律的第一步，进而可以验证加法交换律和结合律。

As a branch of modern algebra , finite fields is an abstract system in algebra which satisfies operational laws such as associative law, commutative law, distributive law etc.

作为近世代数学的一个分支，有限域是一个拥有传统算术四则运算的抽象代数系统，它满足结合律、交换律、分配律、消去律等运算法则。

We cannot always have associative law for operations, for instance, we did not have this law for mixed addition and multiplication,neither for subtraction, 2+3 2+1≠(2+3)(2+1)=5 3,（2-3）- 2≠2-（3-2）,this is why we have to set the rule in operations that "doing inside bracket at first and out side afterwards, doing multiplication and dividing first and addition and subtraction afterwards".

注意运算的结合律并不是永远对的，比如加法和乘法的混合运算就没有结合律，减法也没有，2+3 2+1≠5 3，（2-3）- 2≠2-（3-2），因此我们运算中总是规定先括号内再括号外，先加减后乘除。

The operation laws including:commutative law, associative law, cancellation law, unity of operation, inverse element, and distributive law between two operations,here we just omit them.

这些运算律包括：交换律，结合律，消去律，运算单位元，运算逆元，两个运算之间的分配律等，在此不再一一说明详细过程。

Clearly, the sum of games is a commutative and associative operation, as is the nim sum operation.

无疑，游戏的求和是满足交换律和结合律的运算，nim和运算也是。

Unfortunately, it is not generally possible to determine whether or not an operation is associative simply by glancing at its Cayley table, as is the case with commutativity.

不幸的是，一般不可能象交换律那样通过简单查看凯莱表来确定一个运算是否符合结合律。

The trick about floating point numbers is that although they are extremely useful for representing real-life quantities, operations on them do not obey the arithmetic rules we learned in middle school: associativity, transitivity, commutativity; moreover, many very ordinary-seeming numbers can be represented only approximately with floating point numbers.

For example：有关浮点数的诀窍是，尽管他们是用来代表我们生活中的数，但操作却不符合我们从中学学到的运算法则：结合律，交换律等等，另外许多时候浮点数只是近似值。

Means the parent directory, so this command means to execute "toolchain.sh," which is in the current directory.

代表父目录，所以这个命令就是执行当前目录下的"toolchain.sh"。

Yes,In fact,I'm on our city ream.

是的。事实上我是我们市队的。