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## Homework Statement

Given a set A \in R^m, B_n \in R^m for n \in N, show that

A \ Union {from n = 1 to inf} B_n = Intersection {from n = 1 to inf} (A \ B_n}

## Homework Equations

Same equation as above

## The Attempt at a Solution

I think I have a solution in mind, but I wanted to make sure it is correct:

Say, take x \in (Intersection {from n = 1 to inf} (A \ B_n}), in order for x to be in that set, x must be in A \ B_n for all n \in N.

That implies A \ Union {from n = 1 to inf} B_n, is that correct for the proof? Can I somehow write it out better? I hope someone can fill the gaps in the proof, and any help will be appreciated.