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Say I have a set $E$ with an arbitrary number of elements which are of the form $f$ i.e. $E=\{f(x):x \in\Bbb N\}$ and a set $G$ with an arbitrary number of elements which are of the form $h$ i.e. $G=\{h(a):a\in\Bbb Z\}$.

What would be the general strategy of showing that these two sets are disjoint. I have a basic idea on how to start: Assume for the sake of contradiction that the two sets do have some common elements. How would I then show that this leads to a contradiction allowing me to conclude that $E$ intersection $G$ is the null set. Once again, I just want a general approach to solving this problem. Thanks.

Shubham Johri
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Diamoniner12345
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Suppose there exists an element that is in both sets and reach a contradiction. Or that if $x$ is an element of one of the sets, then it can't be an element of the other set.

Derek Luna
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  • OP asked for just a general approach. This is the best I could possibly think of that answers the question exactly. Why vote to delete it? – Derek Luna Oct 31 '20 at 04:29