Here is a list of fairly standard concepts in mathematics that we will use in this module. You are mostly expected to be familiar with these concepts already.
The symbol := will mean “is defined to be”. Important new words will be in bold.
A set is a collection of distinct elements. If is a set, then the notation means “ is an element of ”.
is the set of integers.
is the set of rational numbers, or fractions. Here we are using set notation; in words it says “the collection of all numbers of the form where are both integers and is not 0.”
If and are sets, then means is a subset of ; in other words, every element of is also an element of . This includes the case when .
If , then means that is strictly bigger than , so it is not equal to . The symbol means that is bigger than or equal to .
We will use logical quantifier symbols (“for all”) and (“there exists”).
is the set of real numbers, including all the rational numbers and the irrational ones (such as , etc…).
is the set of complex numbers is Here the symbol denotes a square root of . So multiplication is defined by .
The product of two numbers (or, more generally, two elements of a field) will be written as , or . For instance:
A function from a set to a set will be written . This means that for every element , we assign an element in , which we call . In other words, if then .