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tgt
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Does {a,b,c}={a,{b,c}}?
Pere Callahan said:No...
tgt said:Does {a,b,c}={a,{b,c}}?
The notation {a,b,c} represents a set with the elements a, b, and c. The notation {a,{b,c}} represents a set with two elements, a and a set containing b and c.
No, they are not the same set. The first set has three elements, while the second set has two elements. The second set also contains a set as one of its elements, while the first set does not.
Yes, a set can contain another set as one of its elements. This is known as a nested set. In the example {a,{b,c}}, the set {b,c} is nested within the larger set.
Understanding the difference between these two notations is important in set theory and mathematics in general. It helps to avoid confusion and ensures accuracy when working with sets and their elements.
No, the elements of a set are not in a specific order. Sets are considered unordered collections of elements, so the order in which the elements are listed does not matter. In the example {a,b,c} and {c,b,a} are the same set.