$Math Proofs: "An alternative notation is sometimes used for the union or intersection of an indexed family of sets."$

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$Math Proofs: "An alternative notation is sometimes used for the union or intersection of an indexed family of sets."$

I'm going through a book on mathematical proof and I'm really confused on what this page means. Specifically, what is i and I and what is the relationship between them?

Thanks.

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https://ibb.co/QvRGFzx

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Anonymous

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$I$ is just a set of indices: could be the naturals, the set of numbers from $1$ to $n$, the reals, or really anything. Not all the families are finite or countable, and it's common to use $I$ as a symbol for an arbitrary set of indices. Then, $i$ is just a generic element of $I$: in the same fashion as you write $n \in \mathbb{N}$ for the generic natural number, you write $i \in I$ for the generic index in $I$.

Alessandro Iraci

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$Math Proofs: "An alternative notation is sometimes used for the union or intersection of an indexed family of sets."$

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