# Halmos-Generalized Version of Associative Law

sammycaps
I posted this in the homework section, but I think it probably belongs here.

So Halmos says in Section 9 on families, "Suppose, for instance, that {Ij} is a family of sets with domain J, say; write K=UjIj and let {Ak} be a family of sets with domain K. Is it then not difficult to prove that, Uk∈ KAk=Uj∈ J(Ui∈ IjAi); this is the generalized version of the associative law for unions

So, I'm just trying to wrap my head around why this is the generalized version of the associative law for unions. Do we have to assign some kind of sequence for the way we take the union over K that somehow transfers to the way we take union over J and Ij? This may be a dumb question, but I'm a bit confused.

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## Answers and Replies

I posted this in the homework section, but I think it probably belongs here.

So Halmos says in Section 9 on families, "Suppose, for instance, that {Ij} is a family of sets with domain J, say; write K=UjIj and let {Ak} be a family of sets with domain K. Is it then not difficult to prove that, Uk∈ KAk=Uj∈ J(Ui∈ IjAi); this is the generalized version of the associative law for unions

So, I'm just trying to wrap my head around why this is the generalized version of the associative law for unions. Do we have to assign some kind of sequence for the way we take the union over K that somehow transfers to the way we take union over J and Ij? This may be a dumb question, but I'm a bit confused.

Uk∈ KAk=Uj∈ J(Ui∈ IjAi)

Above expression is very unclear.

sammycaps
Oh, my bad, when I copy pasted, the formatting was lost in translation. Fixed.