
Partition of a set
The question is to determine whether is a partition of the set .
and , where .
I understand what it means to be a partition, but I'm not sure what , or particularly, means.
Does this mean ? Where I just find any real number pair so that their absolute values are equal?

Re: Partition of a set
Are those sets in disjoint? Nonempty? Does their union equal the whole set (in this case, )? If so, then is a partition of

The only potentially confusing thing here is that the original definition of had redundancies  two different names for the same set  and so that might seem to make it not a partition. However, a set with redundant (even if differently named) elements is the same as the set with unique elements.
i.e. If a = 2, b = 2, then U = {a, b} = { 2, 2 } = { 2 } = { a }.
Likewise: If A = {5, 2}, B = {5, 2}, then V = {A, B} = { {5,2}, {5,2} } = { {5,2} } = { A }.