集合逻辑用语

当谈到集合逻辑时，以下是一些常见的用语和句子：

集合

(set)

元素

(element)

子集

(subset)

包含

(contain)

相等

(equal)

空集

(emptyset)

并集

(union)

交集

(intersection)

补集

(complement)

差集

(setdifference)

幂集

(powerset)

关系

(relation)

等价关系

(equivalencerelation)

偏序关系

(partialorderrelation)

全序关系

(totalorderrelation)

笛卡尔积

(Cartesianproduct)

有限集合

(finiteset)

无限集合

(infiniteset)

可数集合

(countableset)

不可数集合

(uncountableset)

有界集合

(boundedset)

无界集合

(unboundedset)

集合的基数 (cardinality of a set)

空集的基数 (cardinality of the empty set)

自然数集合 (set of natural numbers)

整数集合

(setofintegers)

有理数集合 (set of rational numbers)

实数集合 (set of real numbers)

复数集合 (set of complex numbers)

幂级数集合 (set of power series)

空集是任何集合的子集。 (The empty set is a subset of any set.)

两个集合相等当且仅当它们具有相同的元素。 (Two sets are equal if and only if they have the same elements.)

集合A包含集合B，当且仅当每个B的元素也是A的元素。 (Set A contains set B if and only if every element of B is also an element of A.)

集合A和集合B的并集是由A和B中的所有元素组成的集合。 (The union of sets A and B is the set consisting of all elements in A and B.)

集合A和集合B的交集是由同时属于A和B的元素组成的集合。 (The intersection of sets A and B is the set consisting of elements that belong to both A and B.)

集合A相对于集合B的补集是属于A但不属于B的所有元素构成的集合。 (The complement of set A with respect to set B is the set consisting of all elements that belong to A but not to B.)

集合A和集合B的差集是属于A但不属于B的所有元素构成的集合。 (The set difference of sets A and B is the set consisting of all elements that belong to A but not to B.)

集合A和集合B的笛卡尔积是由A中的元素和B中的元素对构成的集合。 (The Cartesian product of sets A and B is the set consisting of pairs of elements, one from A and one from B.)

集合A是有界集合，如果存在一个实数M，使得对于A中的所有元素x，都有x ≤ M。 (Set A is a bounded set if there exists a real number M such that for every element x in A, x ≤ M.)

集合A是无界集合，如果对于任意实数M，存在A中的元素x，使得x > M。 (Set A is an unbounded set if for any real number M, there exists an element x in A such that x > M.)

集合A的基数表示A中元素的数量。 (The cardinality of set A represents the number of elements in A.)

自然数集合的基数是无穷可数的。 (The cardinality of the set of natural numbers is countably infinite.)

实数集合的基数是不可数的。 (The cardinality of the set of real numbers is uncountable.