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While reading about ordered pairs in the context of the formal language of axiomatic set theory I came across the following in a list of abbreviations. The book is The Foundations of Mathematics by Simpson. Page 93, although I have seen this definition elsewhere.

(singleton) z={x} is an abbreviation for z={x,x}

What does this mean. I always thought that a set with a single member was just a set with a single member. Does singleton have some other meaning.

Thanks.

Matheinste.

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# Set theoretic definition of a singleton.

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