Video: Defining the Universal Set

What is the name of the set containing all elements that has every set, including itself, as a subset?

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Video Transcript

What is the name of the set containing all elements that has every set including itself as a subset?

So we’re looking for the name of a set. And this set should include a couple things. It contains all elements and has every set including itself as a subset. So all of the subsets are every single set and itself. But what is a subset? All the elements of a set are included in another set. So a subset is kind of like a piece of a bigger set or a set that’s exactly the same.

So essentially, this needs to be the largest set. Cause it needs to include all of the elements and all of the subsets, so all of the ones that are smaller than it or equal to it, which is why it says it includes itself. And this set is called the universal set, which is normally written as an italicized 𝑢.

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