Concept
How can a set be an element of another set without being its subset?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Let’s give some examples. Suppose that Q is the set {4, {9, 4}, 2}. Q has three elements here, one of which is itself a set. Now suppose that we let P be the set {4, 9}. Question: is P ∈ Q? The answer is yes: the set {4, 9} (which is the same as the set {9, 4}, just written a different way) is in fact an element of the set Q. Next question: is P ⊆ Q? The answer is no, P is not a subset of Q. If P were a subset of Q, that would imply that every member of P (there are two of them: 9 and 4) is also an element of Q, whereas in fact, only 4 is a member of Q, not 9. Last question: if R is defined to be {2, 4}, is R ⊆ Q? The answer is yes, since both 2 and 4 are also members of Q."
Related Ideas
- How can a set be a member of another set?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How many members does the set V contain?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Can a set containing Han be the same as a set containing another set that includes Han?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Is { Yoda } ∈ J ?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Is the empty set both an element and a subset of X?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What is a power set?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How do membership symbols and fuzzy sets change the idea of belonging?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How are sets written, and what are empty and domain sets?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1