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part of a series of videos im making to support a course that im teaching and introductory proof writing and here were going to start looking at proofs involving sets before we get started i want to recall set builder notation which is like a nice quick way to easily write a set down or what the elements of a set look like so we have a set a which is written in set builder notation like this so weve got two curly braces then weve got a line down the middle sometimes thats a colon and that represents the word such that so over here on the left hand side you have the general shape of an element sometimes you really leave the general shape out and you just put like kind of a symbol to represent the element and the general shape is via context and then over to the right here you need to have the rules that the element must satisfy in order to be in the set now we could write that via the notion of a mathematical statement like this so here weve got a is equal to x and s so s would