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Hilbert's paradox of the Grand Hotel, the Glossary

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets.^[1]

Aleph number

In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. Hilbert's paradox of the Grand Hotel and aleph number are infinity.

See Hilbert's paradox of the Grand Hotel and Aleph number

Axiom of countable choice

The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function.

See Hilbert's paradox of the Grand Hotel and Axiom of countable choice

Bijection

A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the first set (the domain) is mapped to exactly one element of the second set (the codomain).

See Hilbert's paradox of the Grand Hotel and Bijection

Binary number

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one).

See Hilbert's paradox of the Grand Hotel and Binary number

Cardinality

In mathematics, the cardinality of a set is a measure of the number of elements of the set.

See Hilbert's paradox of the Grand Hotel and Cardinality

Coach (bus)

A coach (also known as a coach bus, motorcoach or parlor coach) is a type of bus built for longer-distance service, in contrast to transit buses that are typically used within a single metropolitan region.

See Hilbert's paradox of the Grand Hotel and Coach (bus)

Colloquialism

Colloquialism (also called colloquial language, everyday language, or general parlance) is the linguistic style used for casual (informal) communication.

See Hilbert's paradox of the Grand Hotel and Colloquialism

Countable set

In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Hilbert's paradox of the Grand Hotel and countable set are infinity.

See Hilbert's paradox of the Grand Hotel and Countable set

David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time.

See Hilbert's paradox of the Grand Hotel and David Hilbert

Decimal

The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers.

See Hilbert's paradox of the Grand Hotel and Decimal

Exponentiation

In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power.

See Hilbert's paradox of the Grand Hotel and Exponentiation

George Gamow

George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; Георгий Антонович Гамов; 4 March 1904 – 19 August 1968) was a Soviet and American polymath, theoretical physicist and cosmologist.

See Hilbert's paradox of the Grand Hotel and George Gamow

Infinite set

In set theory, an infinite set is a set that is not a finite set.

See Hilbert's paradox of the Grand Hotel and Infinite set

Infinity

Infinity is something which is boundless, endless, or larger than any natural number.

See Hilbert's paradox of the Grand Hotel and Infinity

Integer factorization

In number theory, integer factorization is the decomposition of a positive integer into a product of integers.

See Hilbert's paradox of the Grand Hotel and Integer factorization

Interleave sequence

In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle.

See Hilbert's paradox of the Grand Hotel and Interleave sequence

Leading zero

A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation.

See Hilbert's paradox of the Grand Hotel and Leading zero

Logical equivalence

In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model.

See Hilbert's paradox of the Grand Hotel and Logical equivalence

Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

See Hilbert's paradox of the Grand Hotel and Mathematical proof

Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.

See Hilbert's paradox of the Grand Hotel and Natural number

Numeral system

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

See Hilbert's paradox of the Grand Hotel and Numeral system

One Two Three... Infinity

One Two Three...

See Hilbert's paradox of the Grand Hotel and One Two Three... Infinity

Pairing function

In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number.

See Hilbert's paradox of the Grand Hotel and Pairing function

Paradox

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation.

See Hilbert's paradox of the Grand Hotel and Paradox

Prime number

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.

See Hilbert's paradox of the Grand Hotel and Prime number

Prime power

In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number.

See Hilbert's paradox of the Grand Hotel and Prime power

Pyramid

A pyramid is a structure whose visible surfaces are triangular in broad outline and converge toward the top, making the appearance roughly a pyramid in the geometric sense.

See Hilbert's paradox of the Grand Hotel and Pyramid

Roll-on/roll-off

Roll-on/roll-off (RORO or ro-ro) ships are cargo ships designed to carry wheeled cargo, such as cars, motorcycles, trucks, semi-trailer trucks, buses, trailers, and railroad cars, that are driven on and off the ship on their own wheels or using a platform vehicle, such as a self-propelled modular transporter.

See Hilbert's paradox of the Grand Hotel and Roll-on/roll-off

Set (mathematics)

In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

See Hilbert's paradox of the Grand Hotel and Set (mathematics)

Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

See Hilbert's paradox of the Grand Hotel and Subset

Thought experiment

A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.

See Hilbert's paradox of the Grand Hotel and Thought experiment

Transfinite number

In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers.

See Hilbert's paradox of the Grand Hotel and Transfinite number

Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle.

See Hilbert's paradox of the Grand Hotel and Triangular number

Viking Press

Viking Press (formally Viking Penguin, also listed as Viking Books) is an American publishing company owned by Penguin Random House.

See Hilbert's paradox of the Grand Hotel and Viking Press

References

[1] https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

Also known as Grand hotel paradox, Hilbert Hotel, Hilbert grand hotel, Hilbert hotel paradox, Hilbert infinite hotel, Hilbert paradox, Hilbert paradox of the Grand Hotel, Hilbert's Grand Hotel, Hilbert's Grand Hotel paradox, Hilbert's Hotel, Hilbert's hoteal, Hilbert's paradox, Hilberts hotel, Hotel Hilbert, Hotel Infinity, Hotel paradox, Infinite hotel, Infinity hotel.

Hilbert's paradox of the Grand Hotel, the Glossary

Table of Contents

See also

1925 introductions

David Hilbert

Eponymous paradoxes

Logical paradoxes

Mathematical paradoxes

Paradoxes of infinity

Paradoxes of set theory

Supertasks

References