What exactly is meant by a family of neighborhoods?

I’m currently self studying Mathematical Analysis for AI and I stumbeled upon the notion of neighborhoods, and families of neighborhoods. Since the definition in the book states that for the real number x there exists an epsilon such that (x – epsilon, x + epsilon) is a subset of the neighborhood V, I’m assuming that there’s an infinite amount of epsilons inside of V and hence an infinite amount of subsets of V. It’s hard for me to understand how there can be infinite amount of neighborhoods inside the family of neighborhoods.

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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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