set and non set example
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The set S= {1} with just one element is an example of a nonempty set. S so defined is also a singleton set. The set S = {1,4,5} is a nonempty set. The set of all real numbers is another example of a nonempty set.
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The most famous example of this is the class of all sets, which is not itself a set. ... That said, there are many other collections of mathematical objects that also can't be sets, for essentially the exact same reason as the class of all sets isn't a set. These include: The class of all groups.
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