User:Peter Schmitt/Notes

Cardinality [r]: The size, i.e., the number of elements, of a (possibly infinite) set. ^[e]
Countable set [r]: A set with as many elements as there are natural numbers, or less. ^[e]

Countable [r]: In mathematics, a property of sets — see: Countable set (A set with as many elements as there are natural numbers, or less.) ^[e]

Uncountable [r]: In mathematics, a property of sets — see: Countable set (A set with as many elements as there are natural numbers, or less.) ^[e]

Uncountable set [r]: A set with more elements than there are natural numbers. (See: Countable set.) ^[e]

Transfinite number [r]: An infinite number, either a cardinal number or an ordinal number. ^[e]
Cardinal number [r]: The generalization of natural numbers (as means to count the elements of a set) to infinite sets. ^[e]

Aleph-0 [r]: Cardinality (size) of the set of all natural numbers. ^[e]

Aleph-1 [r]: Add brief definition or description

Ordinal number [r]: The generalization of natural numbers (as means to order sets by size) to infinite sets. ^[e]
Infinity [r]: Add brief definition or description

Infinite [r]: Greater in size (number of elements, length, area, etc.) than any natural number ^[e]

Infinite set [r]: The number of its elements is larger than any natural number. (See: Finite set.) ^[e]
Finite set [r]: The number of its elements is a natural number (0,1,2,3,...) ^[e]

Finite [r]: Bounded (or limited) in size (length, area, etc., or number of elements) by a natural number ^[e]

Finite and infinite [r]: The distinction between bounded and unbounded in size (number of elements, length, area, etc.) ^[e]
Hilbert's hotel [r]: A fictional story which illustrates certain properties of infinite sets. ^[e]
Galileo's paradox [r]: The observation that there are fewer perfect squares than natural numbers but also equally many. ^[e]
Continuum hypothesis [r]: A statement about the size of the continuum, i.e., the number of elements in the set of real numbers. ^[e]
Zero (mathematics) [r]: The number of elements in an empty set, and a digit or symbol. ^[e] 0 0 (number) zero zero (disambiguation)

Neighbourhood (topology) [r]: In a topological space, a set containing a given point in its interior, expressing the idea of points "near" this point. ^[e]

Boundary point [r]: (of a set) In geometry and topology, a point such that every neighbourhood contains both points in the set and points not in the set. ^[e]

Clopen [r]: In topology, a combination of closed and open (clopen set). ^[e]

Clopen set [r]: In topology, a set with empty boundary which therefore is both closed and open. ^[e]

Open set [r]: In geometry and topology, a set that does not contain any of its boundary points. ^[e]

Closed set [r]: In geometry and topology, a set that contains its boundary; the complement of an open set. ^[e]

Quantile [r]: A statistical parameter that divides the range of a variable (those less and those greater than it) according to a given probability. ^[e]