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October 12, 2018 sets

Families of Sets and `Generalized' Set Operations

By A Cooper Finite Set Operations The operations and apply to two sets; we can however use them to combine more than one set. If we have a...

October 10, 2018 sets

Set-Builder Notation

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

October 10, 2018 sets

The Element's-Eye View

By A Cooper 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...

October 10, 2018 sets

Set Operations and Subsets

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

September 17, 2018 sets

Sets

By A Cooper 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...