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.

Read more about Infinite Set: Properties, History

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

Robertson–Seymour Theorem - Statement

... The minor relationship forms a partial order on the

... 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

... 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

... 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

... 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.)

Main Site Subjects

Related Subjects

Related Phrases

Related Words