Sets and notation

Finite sets given some way of representing elements of a set (i.e., of writing them down), we will write down finite sets of such elements as lists separated by commas and delimited by "curly braces" Ex: { 1, 2, 3 } Ex: { Bill, Steve, Marc }

Sets and notation

	Finite sets
	Infinite sets when we want to indicate an infinite set (without writing it all out), we use the same notation but fill in a suggestive sequence of values, and then use an ellipsis Ex: { 0, 2, 4, 8, ... } Ex: { 1, 17, 31, 128, ... }

Sets and notation

	Finite sets
	Infinite sets
	Zermelo-Frankel notation another way to describe an infinite set with finite notation is to describe it by way of some property or predicate that describes its members Ex: { (x,y) | y = 2 * x } Ex: { p | p was a president of the United States }

Sets and notation

	Finite sets
	Infinite sets
	Zermelo-Frankel notation
	Sequences and tuples a sequence differs from a set in that its components are ordered and may be repeated (the elements of a set are unordered and unique). We often refer to sequences of length n as n-tuples and, for n=2, as pairs Ex: (3, 5, 3)

Sets and notation

	Finite sets
	Infinite sets
	Zermelo-Frankel notation
	Sequences and tuples
	Names for some specific sets we sometimes give names to useful sets; the names can then be used anywhere that any other sort of expression denoting a set could be used Ex: N = the set of natural numbers { 0, 1, 2, ... } Ex: Z = the set of integers { ..., -2, -1, 0, 1, 2, ... }