cardinalityn.1
/ˌkɑːdᵻˈnalᵻti/, U.S. /ˌkɑrdəˈnælədi/, /ˌkɑrdnˈælədi/ rare in later use.
The office of cardinal; = cardinalate n. 1. Also: the condition of being a cardinal.
ΘΚΠ
society > faith > church government > member of the clergy > clerical superior > cardinal > [noun] > office of
cardinalship?a1425
cardinality1514
red hat1522
cardinalate1601
purple1670
cardinalric1688
1514 T. Wolsey Let. in State Papers Henry VIII (P.R.O.: SP 1/9) f. 95 The dyllygent solycytyng [with the] popys holllynes for the determynyng of the Cardynalyte.
1525 Ld. Berners tr. J. Froissart Cronycles II. cxcvi. [cxcii.] 605 All his Cardynalles to be putte out of their Cardynalyties [Fr. cardinalité].
1620 N. Brent tr. P. Sarpi Hist. Councel of Trent vii. 658 The Archbishop of Otranto, and others, who aimed at the Cardinalitie.
2019 @Zemyla 19 Oct. in twitter.com (accessed 6 July 2020) The Pope can appoint secret cardinals without telling anyone, not even the person they're appointing. Though it only works if they reveal the cardinality before they die.
This entry has been updated (OED Third Edition, June 2021; most recently modified version published online December 2021).
cardinalityn.2
/ˌkɑːdᵻˈnalᵻti/, U.S. /ˌkɑrdəˈnælədi/, /ˌkɑrdnˈælədi/ Mathematics.
1. The quality of being a cardinal number; the property of having a certain cardinal numeral. Now rare.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [noun] > cardinal > property of
cardinality1856
1856 R. G. Latham Logic in its Applic. to Lang. 248 To this extent, then, the relation between the cardinality and ordinality of the numerals is peculiar.
1935 Mind 44 343 We may imagine set out before us all the examples, of whatever cardinality, involving a single dyadic relation.
2. The number of elements of a set; the equivalence class of a set under the relation that there exists a one-to-one mapping between members of any two sets in the same class.
ΚΠ
1926 Proc. London Math. Soc. 25 116 By a general law φ we shall mean any postulate of the form ‘If α be any subset of the elements of K of cardinality n, then ψ(α, R)’, where ψ is any logical function of the elements of α and of no other K-elements.
1948 Jrnl. Symbolic Logic 13 199 For the sake of simplicity, we shall postulate that the Boolean set B has cardinality 2. Its only elements will be 1 and 0.
2011 P. M. Higgins Numbers: Very Short Introd. vii. 91 In passing from the rationals to the reals, we are moving from one set to another of higher cardinality as mathematicians put it.
This entry has been updated (OED Third Edition, June 2021; most recently modified version published online December 2021).
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