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Set-Builder Notation

Recall that, by definition, being a set is equivalent to ``" being an open sentence. This means that the theory of sets and the theory...

The Element's-Eye View

There are three things to keep in mind when it comes to set-theory proofs (which most of our proofs hereafter will be): Sets are defined...

Set Operations and Subsets

Just like we defined logical formulae by giving truth tables, we can define set formulae by giving a criterion for membership. Definition. Given sets ,...

Sets

In our quest to reason about quantities and relationships, we'd like to handle quantities that are a bit more general than integers (real numbers, for...