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]