Infinity

thumb|The Sierpiński triangle contains infinitely many (scaled-down) copies of itself. Infinity is something which is boundless, limitless, endless. It is denoted by , called the infinity symbol.

one-dimensional infinite non-curved geometric object

Eternity, also referred to as sempiternity or forever, is time with no end i.e. infinite.

English mathematician (*1616 – †1703)

humorously stated theorem that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will surely type a given text, such as the complete works of William Shakespeare.

class=skin-invert-image|450px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (ε = 1/ω)

set with the same cardinality as some subset of the set of natural numbers

hypothesis that no set has a cardinality between that of the integers and that of the real numbers

the result yielded by a real number when divided by zero

argument that posits that humans bet with their lives that God either exists or does not

proof technique in set theory

alef symbol (U+2135) or aleph, written left-to-right as the mathemical symbol ‹ℵ› for the first transfinite cardinal (countable); ordered sequence of transfinite numbers used to represent the cardinality (or size) of infinite countable sets

set with cardinal number larger than that of the set of all natural numbers

ancient Egyptian deity

thought experiment proposed by David Hilbert

theorem that the number of prime numbers is infinite

a totally ordered proper class containing the real numbers as well as hyperreal numbers such as infinity and infinitesimals.

element of a nonstandard model of the reals, which can be infinite or infinitesimal

ancient Armenian national symbol and a symbol of the national identity of the Armenian people

mathematical symbol ∞ (U+221E), lemniscate

extension of the reals by +∞ and −∞

axiom asserting that the set of natural numbers exists

limiting point in some geometric spaces

cardinality of the set of real numbers

260px|thumb|A partition of the Euclidean line into infinitely many equal-length segments can be understood as a regular apeirogon. In geometry, an apeirogon () or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case of infinite polytopes. In some literature, the term "apeirogon" may refer only to the regular apeirogon, with an infinite dihedral group of symmetries.

alternative formulation of calculus using a logically rigorous notion of infinitesimal numbers

Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as existing.

set whose elements are the real numbers

ordered sequence of transfinite numbers used to represent the cardinality (or size) of continuous sets

Latin phrase

parallel mirrors, creating reflections that appear to recede to infinity

mathematical concept – an extension of the idea of infinity

philosophical concept

infinite-dimensional cube with a compact topology

Apeirophobia () (from ) is the specific phobia of infinity, eternity, endlessness, or the uncountable and is also known as the fear of infinity, the fear of eternity, or the fear of endlessness, causing discomfort and sometimes panic attacks from intrusive thoughts of the infinity. It normally starts in adolescence or earlier and it is currently not known how it normally develops over time. Apeirophobia may be caused by existential dread about eternal life or oblivion following death. Due to this, it is often connected with thanatophobia (the phobia of death), chronophobia (the phobia of time

philosophical doctrine

concept in geometry and topology

concept of infinite entities as given, actual and completed objects rather than non-terminating processes

point at infinity in hyperbolic geometry

generalized natural number

Infinitism is the view that knowledge may be justified by an infinite chain of reasons. It belongs to epistemology, the branch of philosophy that considers the possibility, nature, and means of knowledge.

what happens when an unstoppable force meets an immovable object?

Supreme, final, and fundamental power in all reality

In the philosophy of mathematics, ultrafinitism, ultraintuitionism, strict formalism, strict finitism, actualism, predicativism, and strong finitism are various philosophies of mathematics with aspects of finitism and intuitionism. Common to these philosophies is their objection to the totality of number theoretic functions like exponentiation over natural numbers.

Wikimedia disambiguation page

Finiteness, finitude, or being finite, is the state of being limited or having an end, and is a counter to the concept of infinity. Humans are considered to be in this state because of their limited life span, uniformly ending in death. Each natural number is considered to be in this state, because counting up to that number stops when the number is reached. The concept appears across disciplines, from mathematics and linguistics to philosophy, where it is used to describe quantities, structures, and conditions. In mathematics, a set or number is finite if it is limited in size, while in lingu

extension of the set of the real numbers by a point denoted ∞

principle that whatever succeeds for the finite also succeeds for the infinite

In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An example of an infinite hyperinteger is given by the class of the sequence in the ultrapower construction of the hyperreals.