Hello all.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Set theoretic definition of a singleton.

**Physics Forums | Science Articles, Homework Help, Discussion**