Post History
#4: Post edited
by
tommi
·
2025-11-15T08:22:51Z (10 months ago)
clarified further
- The empty set (or the null set) has no elements. Notation: {}
- The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
- The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
- My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
To add more complications: The power set of the empty set has two subsets; the empty set is a subset and the power set is its own subset. One of these has no elements and the other has a single element.- Especially if you are talking, it is really easy to stumble here. I suggest drawings.
- The empty set (or the null set) has no elements. Notation: {}
- The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
- The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
- My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
- To add more complications: The power set of the empty set has two subsets; the empty set is a subset and the power set itself is its own subset, much like any set is its own subset. One of these has no elements and the other has a single element.
- Especially if you are talking, it is really easy to stumble here. I suggest drawings.
#3: Post edited
by
tommi
·
2025-11-15T08:21:56Z (10 months ago)
- The empty set (or the null set) has no elements. Notation: {}
- The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
- The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
- My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
To add more complications: The power set of the power set of the empty set has two subsets; the empty set is there, as is its power set. One of these has no elements and the other has a single element.- Especially if you are talking, it is really easy to stumble here. I suggest drawings.
- The empty set (or the null set) has no elements. Notation: {}
- The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
- The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
- My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
- To add more complications: The power set of the empty set has two subsets; the empty set is a subset and the power set is its own subset. One of these has no elements and the other has a single element.
- Especially if you are talking, it is really easy to stumble here. I suggest drawings.
#2: Post edited
by
tommi
·
2025-11-15T08:18:36Z (10 months ago)
fixed a mistake
- The empty set (or the null set) has no elements. Notation: {}
- The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
- The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
- My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
To add more complications: The power set of the empty set has two subsets; the empty set is there, as is the power set itself. One of these has no elements and the other has a single element.- Especially if you are talking, it is really easy to stumble here. I suggest drawings.
- The empty set (or the null set) has no elements. Notation: {}
- The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
- The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
- My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
- To add more complications: The power set of the power set of the empty set has two subsets; the empty set is there, as is its power set. One of these has no elements and the other has a single element.
- Especially if you are talking, it is really easy to stumble here. I suggest drawings.
#1: Initial revision
by
tommi
·
2025-11-07T17:21:11Z (10 months ago)
The empty set (or the null set) has no elements. Notation: {}
The empty set has a single subset, which is the empty set. Any other set has at least one element in it, so it can not be a subset of the empty set. Hence the empty set is the only subset of itself.
The power set of the empty set consists of all of its subsets, that is, it consists of the empty set. Notation: {{}}. (A set which has a single element which is the empty set. The inner curly brackets are the empty set, while the outer ones are the set that contains the empty set.) The power set of the empty set has a single element.
My guess is that one of you thought about the number of elements of the empty set (0) and the other thought about the number of elements of the power set of the empty set (1). The number of elements of the only subset of the empty set is also zero, but it is a bit of a strange question.
To add more complications: The power set of the empty set has two subsets; the empty set is there, as is the power set itself. One of these has no elements and the other has a single element.
Especially if you are talking, it is really easy to stumble here. I suggest drawings.