# Infinite Set

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are:

• the set of all integers, {..., -1, 0, 1, 2, ...}, is a countably infinite set; and
• the set of all real numbers is an uncountably infinite set.

### Other articles related to "set, infinite, infinite set, infinite sets":

Robertson–Seymour Theorem - Statement
... The minor relationship forms a partial order on the set of all distinct finite undirected graphs, as it obeys the three axioms of partial orders it is reflexive (every graph is a minor ... A preorder is said to form a well-quasi-ordering if it contains neither an infinite descending chain nor an infinite antichain ... the non-negative integers is a well-quasi-ordering, but the same ordering on the set of all integers is not, because it contains the infinite descending chain 0, −1, −2, −3.. ...
Pocket Set Theory - Some PST Theorems
... cannot be a set by Russell's paradox ... The empty class is a set Proof ... Let i be an infinite set, and consider the class ...
Transfinite Number - Definition
... cardinal number and is the cardinality of the infinite set of the natural numbers ... cardinal numbers between aleph-null and the cardinality of the continuum (the set of real numbers) that is to say, aleph-one is the cardinality of ... (If Zermelo–Fraenkel set theory (ZFC) is consistent, then neither the continuum hypothesis nor its negation can be proven from ZFC.) Some authors, including P ...
Dice Cup - Variants - Non-cubic - Rarer Variations
... The full geometric set of "uniform fair dice" (face-transitive) are Platonic solids, the five regular polyhedra 4, 6, 8, 12, 20 sides Catalan solids, the duals of the 13 Archimedean ... They are based on an infinite set of prisms ...
Infinite Set - History
... The first known occurrence of explicitly infinite sets is in Galileo's last book Two New Sciences written while he was under house arrest by the Inquisition ... Galileo argues that the set of squares is the same size as because there is a one-to-one correspondence And yet, as he says, is a proper subset of and even gets ...

### Famous quotes containing the words set and/or infinite:

The time is out of joint. O cursèd spite
That ever I was born to set it right!
William Shakespeare (1564–1616)

Something is infinite if, taking it quantity by quantity, we can always take something outside.
Aristotle (384–322 B.C.)