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pivoxa15
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A,B are sets
A + B=AuB + AnB
Does it make sense to add sets? I know union and intersections are possible.
A + B=AuB + AnB
Does it make sense to add sets? I know union and intersections are possible.
pivoxa15 said:A,B are sets
A + B=AuB + AnB
Does it make sense to add sets? I know union and intersections are possible.
pivoxa15 said:A,B are sets
A + B=AuB + AnB
Does it make sense to add sets? I know union and intersections are possible.
I take that to mean that you want an element that is in both A and B to show up twice in the sum of A and B? The sum then could not be a set since there are no dupllcates in sets. What kind of object do you want the sum to be, a bag, a.k.a. multiset?pivoxa15 said:A,B are sets
A + B=AuB + AnB
Does it make sense to add sets? I know union and intersections are possible.
Oh. So symmetric difference (more) then?robert Ihnot said:I take it that he wants to say: A +B = A union B-A intersection B.
Is this what you meant previously? You seem to have just defined this addition to be union. The symmetric difference is "the set of elements belonging to one but not both of two given sets", i.e., "A union B-A intersection B", which I assume you meant as "(A union B) - (A intersection B)", with "-" denoting set difference (A - B = {x | x in A and x not in B}).robert Ihnot said:If we take the sets {1,2,3} + {2,3,4} = {1,2,3,4}= A U B, which for n=1 to 4 is the whole set. Thus [tex]A\cup B+A\cap B =A\cup B [/tex] (I don't think measure theory has any effect on that.)
this form might be better because it works even if measure(a intersect b) is infinite.CRGreathouse said:Since you say measure theoretic, perhaps you mean measure(a) + measure(b) = measure(a union b) + measure (a intersect b)? (for finitely additive measures, of course!)
It is? Counterexample, please.matt grime said:In what sense is that better? It is clearly wrong.
The union of two sets A and B is the set of all elements that are in either A or B (or both). The intersection of two sets A and B is the set of all elements that are in both A and B.
To add two sets A and B, we first find the union of A and B, which includes all elements in both sets. Then, we find the intersection of A and B, which includes only the elements that are in both sets. Finally, we add the two resulting sets together to get the final result.
Yes, the union and intersection method can be used to add any number of sets together. We simply need to find the union and intersection of all the sets and then add them together.
The union and intersection method is useful in set theory because it allows us to combine and compare sets, and to find the relationships between them. It also helps in understanding the properties and operations of sets.
The commutative property in the union and intersection method states that the order in which we add the sets does not matter. In other words, A+B = B+A for any sets A and B. This is true for both the union and intersection operations.