cardinal

adj 1: serving as an essential component; "a cardinal rule"; "the

central cause of the problem"; "an example that was

fundamental to the argument"; "computers are

fundamental to modern industrial structure" [syn: {central},

{fundamental}, {key}, {primal}]

2: being or denoting a numerical quantity but not order;

"cardinal numbers" [ant: {ordinal}]

n 1: (Roman Catholic Church) one of a group of more than 100

prominent bishops in the Sacred College who advise the

Pope and elect new Popes

2: the number of elements in a mathematical set [syn: {cardinal

number}]

3: a variable color averaging a vivid red [syn: {carmine}]

4: crested thick-billed North American finch having bright red

plumage in the male [syn: {cardinal grosbeak}, {Richmondena

Cardinalis}, {Cardinalis cardinalis}, {redbird}]

cardinality

The number of elements in a set. If two sets

have the same number of elements (i.e. there is a {bijection}

between them) then they have the same cardinality. A

cardinality is thus an {isomorphism class} in the {category}

of sets.

{aleph 0} is defined as the cardinality of the first

{infinite} {ordinal}, {omega} (the number of {natural

number}s).

(1995-03-29)