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Domains and Rules

When are two functions equal? A function is a kind of relation, which means it's a kind of set. So two functions being equal means,...

The Basics of Functions

Definition. A function from a set to a set is a relation which satisfies the following two conditions: , and That is, a function assigns...

Functions

What is a function? The notion of a function is fundamental to mathematics, but like many fundamental aspects of mathematics, its definition was not nailed...

Equivalence Classes

You've actually dealt with modular arithmetic for most of your life: the clock face represents arithmetic with modulus 12. If you've ever served in the...

Equivalence Relations

We ordinarily are completely comfortable writing things like     The symbols and , though, are definitely not the same. One of them, for example,...

Graphing Relations

There are two ways to think about drawing a picture of a relation on a set . if We can draw relations on , because...