What is the translation of " EMPTY SET " in Chinese?

• 空集

Examples of using Empty set in English and their translations into Chinese

Constructs a new, empty set.
构造一个新的、空属性集。

In particular, the empty set and the whole space are closed.
特别的，空集和全空间是闭集。

The only closed sets are the empty set and X.
唯一的闭集是空集和X。

The empty set and X itself are always both closed and open.
空集合及X{\displaystyleX}自身永远都同时是开集合与闭集合。

Question: What is a Null set or empty set?
问题：怎么判断数组是null还是为空?

In any topological space X, the empty set and the whole space X are both clopen.
在任何拓扑空间X中，空集和整个空间X都是闭开集。

Empty sets: A set having no element is called an empty set.
约定，存在一个没有任何元素的集合，称为空集(emptyset)，记为?

If there was no destructive operation before, an empty set is returned.
如果之前没有破坏性操作，则返回一个空集。

Every neighbourhood system for a non empty set A is a filter called the neighbourhood filter for A.
非空集合A的所有邻域系是叫做A的邻域滤子的滤子。

The clear() method removes all values from a set, leaving you with an empty set.
Clear()方法删除集合中所有的值，留下一个空集合。

We will also use the values 0(logical FALSE/the empty set) and 1(logical TRUE/the universe).
我们还使用值0(逻辑假/空集)和1(逻辑真/全集)。

We can extend this schema to include n=0 if we interpret that case as the axiom of empty set.
我们可以扩展这个模式以包括n=0，如果我们把这个情况詮釋为空集公理的話。

Then{[0]}, the set whose only element is the empty set, will belong to S2X;
则{[0]}，是仅含有空集為元素的集合，属于S2X；.

You can create a new, empty set or create a set from a group of selected patches.
您可以创建一个新的空Set或在已选定的Patch组中创建一个Set。

For example, return cached data or a default value such as empty set of recommendations.
例如，返回缓存数据或者默认值，如一组空白的推荐数据。

As a result, the empty set is the unique initial object of the category of sets and functions.
结果，空集是集合和函数的范畴的唯一初始对象。

A topological space X is connected if and only if the only clopen sets are the empty set and X.
拓扑空间X是连通的，当且仅当唯一的闭开集是空集和X。

In this encoding, zero is the empty set(0={}), and 1 is the successor of 0.
在这种编码中，0是空集（0=∅{\displaystyle0=\varnothing}），而1是0的后继：.

In this case, the usual axiom of extensionality would then imply that every ur-element is equal to the empty set.
在这种情况下，平常的外延性公理将蕴涵所有基本元素等于空集。

A common approach is to define the number 0 to be the empty set{}, and the successor S(x) to be x∪{ x}.
一个常见的方法是定义数字0空集{},和后继数S(x)x∪{x}。

The Blackhole storage engine accepts but does not store data, and the retrieval always returns an empty set.
BLACKHOLE存储引擎接受但不存储数据，并且检索总是返回一个空集。

Letters is now an empty set, but is still of type Set<Character>
Letters现在是一个空的Set,但是它依然是Set<Character>类型.

Somewhere along the line, that evolved into“Null Set,” which is a different thing, mathematically, but has a better ring to it than“Empty Set.”.
某处沿线，这演变成“空集，”这是一个不同的东西，在数学上，但有一个更好的环比“空集”。

The set constructor[] denotes the empty set, while[x] denotes the set whose only member is the value of x.
集合构造器[]表示空集，而[x]表示一个集合，它仅有的一个成员是x值。

Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set.
莱布尼茨阐明了我们现在叫做合取、析取、否定、同一、集合包含和空集的首要性质。

(Every element of the empty set is a member of any given set- since the empty set has no elements.).
(空数组中所有元素都符合给定的条件，注：因为空数组没有元素)。

The connection between the two concepts goes further however: in the standard set-theoretic definition of natural numbers, zero is defined as the empty set.
然而，这两者的关系可能更进一步：在标准的自然数的集合论定义中，0被定义为空集。

Here, the open sets consist of the empty set, the whole real line, and all sets generated by half-open intervals of the form a.
这种拓扑的开集由下列点集构成-空集、全集和由全体半开区间a,b生成的集合。