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The concept underlying (almost) all math

We have seen concepts like propositions, predicates, function, and formulas and have seen the value in reasoning over them all at once. But how should we make sense of collections of propositions? Or of functions?

There are various ways to approach this but the most common is the notion of a set. For most mathematicians, the objects they work are built up from sets.

What are sets? We won’t answer that question precisely. But, we will give you enough examples, properties, and constructions that you should gain some intuition for them.

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