An enumeration of an infinite set C, represented as a list c1, c2, ..., ck, ..., means that every element in set C is listed exactly once in the sequence. This sequence or list contains all elements of the set C and each element appears at least once.

Here are the steps to understand this:

1. An infinite set C means that the number of elements in the set is not finite. It can be countably infinite (like the set of all integers) or uncountably infinite (like the set of all real numbers).

2. An enumeration of a set is a listing of all its elements. In this case, the elements are represented as c1, c2, ..., ck, ... . The subscript k represents the position of each element in the list.

3. The ellipsis (...) before and after ck indicates that the list goes on indefinitely, which is consistent with the fact that C is an infinite set.

4. The statement implies that every element in set C appears in the list exactly once. This means that the list contains no duplicates and covers all elements in the set C.

5. Therefore, this list or sequence is a complete enumeration of all elements in the infinite set C.

Question

An enumeration of an infinite set C, represented as a list c1, c2, ..., ck, ..., means that every element in set C is listed exactly once in the sequence. This sequence or list contains all elements of the set C and each element appears at least once.

Here are the steps to understand this:

1. An infinite set C means that the number of elements in the set is not finite. It can be countably infinite (like the set of all integers) or uncountably infinite (like the set of all real numbers).

2. An enumeration of a set is a listing of all its elements. In this case, the elements are represented as c1, c2, ..., ck, ... . The subscript k represents the position of each element in the list.

3. The ellipsis (...) before and after ck indicates that the list goes on indefinitely, which is consistent with the fact that C is an infinite set.

4. The statement implies that every element in set C appears in the list exactly once. This means that the list contains no duplicates and covers all elements in the set C.

5. Therefore, this list or sequence is a complete enumeration of all elements in the infinite set C.

Knowee AI · Accepted Answer

An enumeration of an infinite set C, represented as a list c1, c2, ..., ck, ..., means that every element in set C is listed exactly once in the sequence. This sequence or list contains all elements of the set C and each element appears at least once.

Here are the steps to understand this:

1. An infinite set C means that the number of elements in the set is not finite. It can be countably infinite (like the set of all integers) or uncountably infinite (like the set of all real numbers).

2. An enumeration of a set is a listing of all its elements. In this case, the elements are represented as c1, c2, ..., ck, ... . The subscript k represents the position of each element in the list.

3. The ellipsis (...) before and after ck indicates that the list goes on indefinitely, which is consistent with the fact that C is an infinite set.

4. The statement implies that every element in set C appears in the list exactly once. This means that the list contains no duplicates and covers all elements in the set C.

5. Therefore, this list or sequence is a complete enumeration of all elements in the infinite set C.

If C is an inﬁnite set, a list c1, c2, . . . , ck, . . . is an enumeration ofC i

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