3818:
1722:
70:
1736:
1096:
1236:
478:
830:, which multiplies the first two (one-cell) numbers, dividing by the third, with the intermediate result being a double cell number. This is used when the intermediate result would overflow a single cell.
71:
751:. The first operand (the condition) is evaluated, and if it is true, the result of the entire expression is the value of the second operand, otherwise it is the value of the third operand.
962:
876:
358:
1118:
291:
233:
184:
1706:
is also common). Functions vary widely in the number of arguments, though large numbers can become unwieldy. Some programming languages also offer support for
1275:
The same is true for programming languages, where functions taking several arguments could always be defined as functions taking a single argument of some
2197:
2872:
2955:
2096:
378:
3269:
3427:
1978:
1953:
1926:
1893:
1866:
2215:
3282:
2605:
3287:
3277:
3014:
2867:
2220:
2211:
3423:
2068:
886:
709:
2765:
3520:
3264:
2089:
1091:{\displaystyle {\bar {x}}={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)={\frac {x_{1}+x_{2}+\dots +x_{n}}{n}}}
2825:
2518:
605:
2259:
3781:
3483:
3246:
3241:
3066:
2487:
2171:
1688:
1661:
879:
729:
506:
3776:
3559:
3476:
3189:
3120:
2997:
2239:
777:
755:
3701:
3527:
3213:
2847:
2446:
823:
745:
737:
590:
97:. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and
3579:
3574:
3184:
2923:
2852:
2181:
2082:
1826:
1696:
733:
3847:
3508:
3098:
2492:
2460:
2151:
1305:. In logic and philosophy, predicates or relations accepting a variable number of arguments are called
647:
3842:
3798:
3747:
3644:
3142:
3103:
2580:
2225:
1623:
609:
2254:
1231:{\displaystyle \left(\prod _{i=1}^{n}a_{i}\right)^{\frac {1}{n}}=\ {\sqrt{a_{1}a_{2}\cdots a_{n}}}.}
3639:
3569:
3108:
2960:
2943:
2666:
2146:
721:
534:
307:
1645:
These words are often used to describe anything related to that number (e.g., undenary chess is a
844:
3471:
3448:
3409:
3295:
3236:
2882:
2802:
2646:
2590:
2203:
1253:
arguments can always be considered as a function of a single argument that is an element of some
893:
instructions are ternary (as opposed to only two operands specified in CISC); or higher, such as
667:
620:
90:
249:
3761:
3488:
3466:
3433:
3326:
3172:
3157:
3130:
3081:
2965:
2900:
2725:
2691:
2686:
2560:
2391:
2368:
1692:
1657:
1390:
683:
546:
502:
491:
94:
86:
78:
1943:
1883:
3691:
3544:
3336:
3054:
2790:
2696:
2555:
2540:
2421:
2396:
1793:
1284:
1108:
834:
200:
136:
115:
1856:
928:
the contents of a calculated memory location that is the sum (parenthesis) of the registers
3664:
3626:
3503:
3307:
3147:
3071:
3049:
2877:
2835:
2734:
2701:
2565:
2353:
2264:
1684:
1665:
1481:
1307:
712:
architectures, it is common to have two source operands (and store result in one of them).
157:
1918:
8:
3793:
3684:
3669:
3649:
3606:
3493:
3443:
3369:
3314:
3251:
3044:
3039:
2987:
2755:
2744:
2416:
2316:
2244:
2235:
2231:
2166:
2161:
1765:
1323:
700:
688:
586:
3822:
3591:
3554:
3539:
3532:
3515:
3319:
3301:
3167:
3093:
3076:
3029:
2842:
2751:
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2411:
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2156:
2105:
1852:
1814:
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1727:
1707:
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1276:
582:
538:
127:
In general, functions or operators with a given arity follow the naming conventions of
2775:
1299:
In computer science, a function that accepts a variable number of arguments is called
505:, a function without arguments can be meaningful and not necessarily constant (due to
3817:
3757:
3564:
3374:
3364:
3256:
3137:
2972:
2948:
2729:
2713:
2618:
2595:
2472:
2441:
2406:
2301:
2136:
2064:
1974:
1949:
1922:
1889:
1862:
1770:
1741:
1721:
1700:
1669:
1619:
1468:
1301:
890:
574:
298:
635:, and so forth, the term "singulary" is the correct adjective, rather than "unary".
3771:
3766:
3659:
3616:
3438:
3399:
3394:
3379:
3205:
3162:
3059:
2857:
2807:
2381:
2343:
2059:
2033:
1911:
1760:
1435:
1418:
663:
636:
554:
240:
45:
35:
3752:
3742:
3696:
3679:
3634:
3596:
3498:
3418:
3225:
3152:
3125:
3113:
3019:
2933:
2907:
2862:
2830:
2631:
2433:
2376:
2326:
2291:
2249:
1755:
1410:
1331:
1262:
948:
651:
601:
558:
514:
191:
3737:
3716:
3674:
3654:
3549:
3404:
3002:
2992:
2982:
2977:
2911:
2785:
2661:
2550:
2545:
2523:
2124:
2037:
1820:
1476:
1335:
1101:
671:
578:
566:
550:
526:
132:
3836:
3711:
3389:
2896:
2681:
2671:
2641:
2626:
2296:
1780:
1646:
1254:
562:
3611:
3458:
3359:
3351:
3231:
3179:
3088:
3024:
3007:
2938:
2797:
2656:
2358:
2141:
1823: â Defines the inputs and outputs for a function, subroutine or method
1453:
694:
1710:, i.e., functions syntactically accepting a variable number of arguments.
3721:
3601:
2780:
2770:
2717:
2401:
2321:
2306:
2186:
2131:
1806:
1788:
1457:
1424:
594:
570:
530:
140:
110:
31:
1817: â Declaration of a function's name and type signature but not body
1642:
operands (or parameters), but is often used as a synonym of "polyadic".
2651:
2506:
2477:
2283:
1798:
1449:
1322:
names are commonly used for specific arities, primarily based on Latin
98:
1242:
of the geometric mean is the arithmetic mean of the logarithms of its
708:
are typically used as binary operators with two distinct operands. In
3803:
3706:
2759:
2676:
2636:
2600:
2536:
2348:
2338:
2311:
2074:
1775:
1239:
841:, which will pop three values from the stack and efficiently compute
675:
662:
Most operators encountered in programming and mathematics are of the
542:
3788:
3586:
3034:
2739:
2333:
1909:
Detlefsen, Michael; McCarty, David
Charles; Bacon, John B. (1999).
1831:
1443:
1288:
679:
581:, that however has two parts at a lower level of abstraction), and
494:
can be treated as the output of an operation of arity 0, called a
3384:
2176:
1400:
82:
20:
1998:, Cambridge, Massachusetts: Harvard University Press, p. 13
473:{\textstyle f(x_{1},x_{2},\ldots ,x_{n})=2\prod _{i=1}^{n}x_{i}}
666:
form. For both programming and mathematics, these include the
51:
2274:
2119:
1396:
1319:
1280:
859:
725:
144:
27:
517:
or the whole state of the system (time, free memory, etc.).
1699:; syntactical operators usually have arity 1, 2, or 3 (the
741:
60:
2057:
Burris, Stanley N., and H.P. Sankappanavar, H. P., 1981.
1703:
1257:. However, it may be convenient for notation to consider
54:
1945:
847:
381:
147:
prefix is combined with the -ary suffix. For example:
1935:
1908:
1121:
965:
537:-style languages (not in logical languages), and the
310:
252:
203:
160:
1973:(6th ed.). John Wiley & Sons. p. 507.
1717:
1265:(which are not linear maps on the product space, if
57:
533:and plus, the increment and decrement operators in
48:
1941:
1910:
1230:
1090:
870:
472:
352:
285:
227:
178:
19:"Adicity" redirects here. Not to be confused with
1902:
1249:From a mathematical point of view, a function of
3834:
758:language has a ternary conditional expression,
2024:Oliver, Alex (2004). "Multigrade Predicates".
1942:Cocchiarella, Nino B.; Freund, Max A. (2008).
585:functions in mathematics. In programming the
529:in mathematics and in programming include the
2090:
1845:
1875:
1858:Encyclopaedia of Mathematics, Supplement III
826:language also contains a ternary operator,
650:such as 'is square-shaped' as opposed to a
597:operators are examples of unary operators.
2282:
2097:
2083:
1962:
1851:
1338:. For example, 1-ary is based on cardinal
16:Number of arguments required by a function
1881:
2008:
1948:. Oxford University Press. p. 121.
1885:Handbook of Analysis and Its Foundations
670:, the radix operator, the often omitted
1971:Dictionary of Linguistics and Phonetics
1968:
837:has several ternary operators, such as
724:and its various descendants (including
151:A nullary function takes no arguments.
3835:
2104:
2023:
2013:, Amsterdam: North-Holland, p. 19
2078:
1993:
686:operator. Logical predicates such as
2053:A monograph available free online:
13:
1330:", though some are based on Latin
720:The computer programming language
14:
3859:
2048:
612:) are technically unary, but see
608:(especially those descended from
3816:
1734:
1720:
1342:, rather than from distributive
1311:, anadic, or variably polyadic.
1294:
646:is sometimes used to describe a
623:, the Latin distributives being
606:functional programming languages
509:). Such functions may have some
44:
1888:. Academic Press. p. 356.
1680:+1 considered as a relation.)
1261:-ary functions, as for example
781:
759:
2060:A Course in Universal Algebra.
2017:
2002:
1987:
1395:a function without arguments,
1314:
972:
430:
385:
332:
314:
268:
256:
213:
207:
167:
164:
1:
3777:History of mathematical logic
1838:
871:{\textstyle x^{y}{\bmod {z}}}
642:In philosophy, the adjective
573:(the principal square root),
353:{\displaystyle f(x,y,z)=2xyz}
3702:Primitive recursive function
2071:. Especially pp. 22â24.
1649:with an 11Ă11 board, or the
1371:Example in computer science
746:ternary conditional operator
654:such as 'is the sister of'.
7:
1827:Univariate and multivariate
1713:
122:
101:, arity may also be called
10:
3864:
2766:SchröderâBernstein theorem
2493:Monadic predicate calculus
2152:Foundations of mathematics
2009:Robinson, Abraham (1966),
1664:) is the dimension of the
744:, and others) provide the
715:
613:
485:
286:{\displaystyle f(x,y)=2xy}
18:
3812:
3799:Philosophy of mathematics
3748:Automated theorem proving
3730:
3625:
3457:
3350:
3202:
2919:
2895:
2873:Von NeumannâBernaysâGödel
2818:
2712:
2616:
2514:
2505:
2432:
2367:
2273:
2195:
2112:
1477:triple product of vectors
894:
780:the equivalent would be,
657:
2038:10.1093/mind/113.452.609
1994:Quine, W. V. O. (1940),
1882:Schechter, Eric (1997).
939:
520:
3449:Self-verifying theories
3270:Tarski's axiomatization
2221:Tarski's undefinability
2216:incompleteness theorems
1969:Crystal, David (2008).
1861:. Springer. p. 3.
1672:. (A function of arity
1283:, or in languages with
668:multiplication operator
639:follows Quine's usage.
301:takes three arguments.
228:{\displaystyle f(x)=2x}
3823:Mathematics portal
3434:Proof of impossibility
3082:propositional variable
2392:Propositional calculus
1581:denary (alt. decenary)
1566:novenary (alt. nonary)
1368:Example in mathematics
1285:higher-order functions
1232:
1148:
1092:
1016:
872:
503:functional programming
474:
459:
354:
287:
229:
180:
113:, it is usually named
3692:Kolmogorov complexity
3645:Computably enumerable
3545:Model complete theory
3337:Principia Mathematica
2397:Propositional formula
2226:BanachâTarski paradox
2011:Non-standard Analysis
1917:. Routledge. p.
1794:Valency (linguistics)
1668:in the corresponding
1365:Adicity (Greek based)
1346:that would result in
1326:meaning "in group of
1233:
1128:
1109:positive real numbers
1093:
996:
873:
475:
439:
355:
288:
243:takes two arguments.
230:
181:
179:{\displaystyle f()=2}
3640:ChurchâTuring thesis
3627:Computability theory
2836:continuum hypothesis
2354:Square of opposition
2212:Gödel's completeness
1691:distinction between
1685:computer programming
1596:multary and multiary
1482:conditional operator
1324:distributive numbers
1119:
963:
845:
379:
368:-ary function takes
308:
250:
201:
194:takes one argument.
158:
3794:Mathematical object
3685:P versus NP problem
3650:Computable function
3444:Reverse mathematics
3370:Logical consequence
3247:primitive recursive
3242:elementary function
3015:Free/bound variable
2868:TarskiâGrothendieck
2387:Logical connectives
2317:Logical equivalence
2167:Logical consequence
1853:Hazewinkel, Michiel
1766:Theory of relations
1687:, there is often a
1362:Arity (Latin based)
955:real numbers is an
920:, which will load (
880:arbitrary precision
77:) is the number of
3592:Transfer principle
3555:Semantics of logic
3540:Categorical theory
3516:Non-standard model
3030:Logical connective
2157:Information theory
2106:Mathematical logic
1996:Mathematical logic
1815:Function prototype
1751:Logic of relatives
1728:Mathematics portal
1708:variadic functions
1651:Millenary Petition
1228:
1088:
868:
682:operator, and the
652:two-place relation
648:one-place relation
470:
350:
283:
225:
176:
3848:Universal algebra
3830:
3829:
3762:Abstract category
3565:Theories of truth
3375:Rule of inference
3365:Natural deduction
3346:
3345:
2891:
2890:
2596:Cartesian product
2501:
2500:
2407:Many-valued logic
2382:Boolean functions
2265:Russell's paradox
2240:diagonal argument
2137:First-order logic
2063:Springer-Verlag.
1980:978-1-405-15296-9
1955:978-0-19-536658-7
1928:978-0-415-21375-2
1913:Logic from A to Z
1895:978-0-12-622760-4
1868:978-1-4020-0198-7
1771:Signature (logic)
1742:Philosophy portal
1670:Cartesian product
1629:
1628:
1620:variadic function
1223:
1180:
1172:
1086:
989:
975:
891:assembly language
600:All functions in
591:address reference
575:complex conjugate
501:Also, outside of
496:nullary operation
3855:
3843:Abstract algebra
3821:
3820:
3772:History of logic
3767:Category of sets
3660:Decision problem
3439:Ordinal analysis
3380:Sequent calculus
3278:Boolean algebras
3218:
3217:
3192:
3163:logical/constant
2917:
2916:
2903:
2826:ZermeloâFraenkel
2577:Set operations:
2512:
2511:
2449:
2280:
2279:
2260:LöwenheimâSkolem
2147:Formal semantics
2099:
2092:
2085:
2076:
2075:
2042:
2041:
2032:(452): 609â681.
2021:
2015:
2014:
2006:
2000:
1999:
1991:
1985:
1984:
1966:
1960:
1959:
1939:
1933:
1932:
1916:
1906:
1900:
1899:
1879:
1873:
1872:
1849:
1761:Ternary relation
1744:
1739:
1738:
1737:
1730:
1725:
1724:
1701:ternary operator
1419:additive inverse
1353:
1352:
1332:cardinal numbers
1271:
1263:multilinear maps
1237:
1235:
1234:
1229:
1224:
1222:
1217:
1216:
1215:
1203:
1202:
1193:
1192:
1182:
1178:
1174:
1173:
1165:
1163:
1159:
1158:
1157:
1147:
1142:
1097:
1095:
1094:
1089:
1087:
1082:
1081:
1080:
1062:
1061:
1049:
1048:
1038:
1033:
1029:
1028:
1027:
1026:
1015:
1010:
990:
982:
977:
976:
968:
959:-ary function:
935:
931:
927:
924:) into register
923:
919:
918:
915:
912:
909:
906:
903:
900:
897:
877:
875:
874:
869:
867:
866:
857:
856:
840:
829:
818:
817:
814:
811:
808:
805:
802:
799:
796:
793:
790:
787:
784:
775:
774:
771:
768:
765:
762:
750:
637:Abraham Robinson
587:two's complement
577:(unary of "one"
515:global variables
479:
477:
476:
471:
469:
468:
458:
453:
429:
428:
410:
409:
397:
396:
359:
357:
356:
351:
299:ternary function
292:
290:
289:
284:
234:
232:
231:
226:
185:
183:
182:
177:
76:
75:
74:
73:
66:
63:
62:
59:
56:
53:
50:
36:computer science
3863:
3862:
3858:
3857:
3856:
3854:
3853:
3852:
3833:
3832:
3831:
3826:
3815:
3808:
3753:Category theory
3743:Algebraic logic
3726:
3697:Lambda calculus
3635:Church encoding
3621:
3597:Truth predicate
3453:
3419:Complete theory
3342:
3211:
3207:
3203:
3198:
3190:
2910: and
2906:
2901:
2887:
2863:New Foundations
2831:axiom of choice
2814:
2776:Gödel numbering
2716: and
2708:
2612:
2497:
2447:
2428:
2377:Boolean algebra
2363:
2327:Equiconsistency
2292:Classical logic
2269:
2250:Halting problem
2238: and
2214: and
2202: and
2201:
2196:Theorems (
2191:
2108:
2103:
2051:
2046:
2045:
2022:
2018:
2007:
2003:
1992:
1988:
1981:
1967:
1963:
1956:
1940:
1936:
1929:
1907:
1903:
1896:
1880:
1876:
1869:
1850:
1846:
1841:
1836:
1756:Binary relation
1740:
1735:
1733:
1726:
1719:
1716:
1676:thus has arity
1656:The arity of a
1593:more than 2-ary
1336:ordinal numbers
1317:
1297:
1266:
1218:
1211:
1207:
1198:
1194:
1188:
1184:
1183:
1181:
1164:
1153:
1149:
1143:
1132:
1127:
1123:
1122:
1120:
1117:
1116:
1115:-ary function:
1100:Similarly, the
1076:
1072:
1057:
1053:
1044:
1040:
1039:
1037:
1022:
1018:
1017:
1011:
1000:
995:
991:
981:
967:
966:
964:
961:
960:
949:arithmetic mean
945:
933:
929:
925:
921:
916:
913:
910:
907:
904:
901:
898:
895:
862:
858:
852:
848:
846:
843:
842:
838:
827:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
782:
772:
769:
766:
763:
760:
748:
718:
660:
602:lambda calculus
559:fractional part
527:unary operators
523:
488:
464:
460:
454:
443:
424:
420:
405:
401:
392:
388:
380:
377:
376:
309:
306:
305:
251:
248:
247:
241:binary function
202:
199:
198:
159:
156:
155:
133:numeral systems
125:
69:
68:
47:
43:
24:
17:
12:
11:
5:
3861:
3851:
3850:
3845:
3828:
3827:
3813:
3810:
3809:
3807:
3806:
3801:
3796:
3791:
3786:
3785:
3784:
3774:
3769:
3764:
3755:
3750:
3745:
3740:
3738:Abstract logic
3734:
3732:
3728:
3727:
3725:
3724:
3719:
3717:Turing machine
3714:
3709:
3704:
3699:
3694:
3689:
3688:
3687:
3682:
3677:
3672:
3667:
3657:
3655:Computable set
3652:
3647:
3642:
3637:
3631:
3629:
3623:
3622:
3620:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3584:
3583:
3582:
3577:
3572:
3562:
3557:
3552:
3550:Satisfiability
3547:
3542:
3537:
3536:
3535:
3525:
3524:
3523:
3513:
3512:
3511:
3506:
3501:
3496:
3491:
3481:
3480:
3479:
3474:
3467:Interpretation
3463:
3461:
3455:
3454:
3452:
3451:
3446:
3441:
3436:
3431:
3421:
3416:
3415:
3414:
3413:
3412:
3402:
3397:
3387:
3382:
3377:
3372:
3367:
3362:
3356:
3354:
3348:
3347:
3344:
3343:
3341:
3340:
3332:
3331:
3330:
3329:
3324:
3323:
3322:
3317:
3312:
3292:
3291:
3290:
3288:minimal axioms
3285:
3274:
3273:
3272:
3261:
3260:
3259:
3254:
3249:
3244:
3239:
3234:
3221:
3219:
3200:
3199:
3197:
3196:
3195:
3194:
3182:
3177:
3176:
3175:
3170:
3165:
3160:
3150:
3145:
3140:
3135:
3134:
3133:
3128:
3118:
3117:
3116:
3111:
3106:
3101:
3091:
3086:
3085:
3084:
3079:
3074:
3064:
3063:
3062:
3057:
3052:
3047:
3042:
3037:
3027:
3022:
3017:
3012:
3011:
3010:
3005:
3000:
2995:
2985:
2980:
2978:Formation rule
2975:
2970:
2969:
2968:
2963:
2953:
2952:
2951:
2941:
2936:
2931:
2926:
2920:
2914:
2897:Formal systems
2893:
2892:
2889:
2888:
2886:
2885:
2880:
2875:
2870:
2865:
2860:
2855:
2850:
2845:
2840:
2839:
2838:
2833:
2822:
2820:
2816:
2815:
2813:
2812:
2811:
2810:
2800:
2795:
2794:
2793:
2786:Large cardinal
2783:
2778:
2773:
2768:
2763:
2749:
2748:
2747:
2742:
2737:
2722:
2720:
2710:
2709:
2707:
2706:
2705:
2704:
2699:
2694:
2684:
2679:
2674:
2669:
2664:
2659:
2654:
2649:
2644:
2639:
2634:
2629:
2623:
2621:
2614:
2613:
2611:
2610:
2609:
2608:
2603:
2598:
2593:
2588:
2583:
2575:
2574:
2573:
2568:
2558:
2553:
2551:Extensionality
2548:
2546:Ordinal number
2543:
2533:
2528:
2527:
2526:
2515:
2509:
2503:
2502:
2499:
2498:
2496:
2495:
2490:
2485:
2480:
2475:
2470:
2465:
2464:
2463:
2453:
2452:
2451:
2438:
2436:
2430:
2429:
2427:
2426:
2425:
2424:
2419:
2414:
2404:
2399:
2394:
2389:
2384:
2379:
2373:
2371:
2365:
2364:
2362:
2361:
2356:
2351:
2346:
2341:
2336:
2331:
2330:
2329:
2319:
2314:
2309:
2304:
2299:
2294:
2288:
2286:
2277:
2271:
2270:
2268:
2267:
2262:
2257:
2252:
2247:
2242:
2230:Cantor's
2228:
2223:
2218:
2208:
2206:
2193:
2192:
2190:
2189:
2184:
2179:
2174:
2169:
2164:
2159:
2154:
2149:
2144:
2139:
2134:
2129:
2128:
2127:
2116:
2114:
2110:
2109:
2102:
2101:
2094:
2087:
2079:
2073:
2072:
2050:
2049:External links
2047:
2044:
2043:
2016:
2001:
1986:
1979:
1961:
1954:
1934:
1927:
1901:
1894:
1874:
1867:
1843:
1842:
1840:
1837:
1835:
1834:
1829:
1824:
1821:Type signature
1818:
1812:
1804:
1796:
1791:
1786:
1778:
1773:
1768:
1763:
1758:
1753:
1747:
1746:
1745:
1731:
1715:
1712:
1627:
1626:
1617:
1614:
1611:
1609:
1605:
1604:
1602:
1600:
1597:
1594:
1590:
1589:
1587:
1585:
1582:
1579:
1575:
1574:
1572:
1570:
1567:
1564:
1560:
1559:
1557:
1555:
1552:
1549:
1545:
1544:
1542:
1540:
1537:
1534:
1530:
1529:
1527:
1525:
1522:
1519:
1515:
1514:
1512:
1510:
1507:
1504:
1500:
1499:
1497:
1495:
1492:
1489:
1485:
1484:
1479:
1474:
1471:
1466:
1462:
1461:
1446:
1441:
1438:
1433:
1429:
1428:
1421:
1416:
1413:
1408:
1404:
1403:
1393:
1387:
1384:
1379:nullary (from
1377:
1373:
1372:
1369:
1366:
1363:
1360:
1316:
1313:
1296:
1293:
1277:composite type
1227:
1221:
1214:
1210:
1206:
1201:
1197:
1191:
1187:
1177:
1171:
1168:
1162:
1156:
1152:
1146:
1141:
1138:
1135:
1131:
1126:
1102:geometric mean
1085:
1079:
1075:
1071:
1068:
1065:
1060:
1056:
1052:
1047:
1043:
1036:
1032:
1025:
1021:
1014:
1009:
1006:
1003:
999:
994:
988:
985:
980:
974:
971:
944:
938:
865:
861:
855:
851:
717:
714:
678:operator, the
674:operator, the
672:exponentiation
659:
656:
579:complex number
567:absolute value
522:
519:
487:
484:
483:
482:
481:
480:
467:
463:
457:
452:
449:
446:
442:
438:
435:
432:
427:
423:
419:
416:
413:
408:
404:
400:
395:
391:
387:
384:
362:
361:
360:
349:
346:
343:
340:
337:
334:
331:
328:
325:
322:
319:
316:
313:
295:
294:
293:
282:
279:
276:
273:
270:
267:
264:
261:
258:
255:
237:
236:
235:
224:
221:
218:
215:
212:
209:
206:
192:unary function
188:
187:
186:
175:
172:
169:
166:
163:
124:
121:
15:
9:
6:
4:
3:
2:
3860:
3849:
3846:
3844:
3841:
3840:
3838:
3825:
3824:
3819:
3811:
3805:
3802:
3800:
3797:
3795:
3792:
3790:
3787:
3783:
3780:
3779:
3778:
3775:
3773:
3770:
3768:
3765:
3763:
3759:
3756:
3754:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3735:
3733:
3729:
3723:
3720:
3718:
3715:
3713:
3712:Recursive set
3710:
3708:
3705:
3703:
3700:
3698:
3695:
3693:
3690:
3686:
3683:
3681:
3678:
3676:
3673:
3671:
3668:
3666:
3663:
3662:
3661:
3658:
3656:
3653:
3651:
3648:
3646:
3643:
3641:
3638:
3636:
3633:
3632:
3630:
3628:
3624:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3585:
3581:
3578:
3576:
3573:
3571:
3568:
3567:
3566:
3563:
3561:
3558:
3556:
3553:
3551:
3548:
3546:
3543:
3541:
3538:
3534:
3531:
3530:
3529:
3526:
3522:
3521:of arithmetic
3519:
3518:
3517:
3514:
3510:
3507:
3505:
3502:
3500:
3497:
3495:
3492:
3490:
3487:
3486:
3485:
3482:
3478:
3475:
3473:
3470:
3469:
3468:
3465:
3464:
3462:
3460:
3456:
3450:
3447:
3445:
3442:
3440:
3437:
3435:
3432:
3429:
3428:from ZFC
3425:
3422:
3420:
3417:
3411:
3408:
3407:
3406:
3403:
3401:
3398:
3396:
3393:
3392:
3391:
3388:
3386:
3383:
3381:
3378:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3357:
3355:
3353:
3349:
3339:
3338:
3334:
3333:
3328:
3327:non-Euclidean
3325:
3321:
3318:
3316:
3313:
3311:
3310:
3306:
3305:
3303:
3300:
3299:
3297:
3293:
3289:
3286:
3284:
3281:
3280:
3279:
3275:
3271:
3268:
3267:
3266:
3262:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3235:
3233:
3230:
3229:
3227:
3223:
3222:
3220:
3215:
3209:
3204:Example
3201:
3193:
3188:
3187:
3186:
3183:
3181:
3178:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3155:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3132:
3129:
3127:
3124:
3123:
3122:
3119:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3096:
3095:
3092:
3090:
3087:
3083:
3080:
3078:
3075:
3073:
3070:
3069:
3068:
3065:
3061:
3058:
3056:
3053:
3051:
3048:
3046:
3043:
3041:
3038:
3036:
3033:
3032:
3031:
3028:
3026:
3023:
3021:
3018:
3016:
3013:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2990:
2989:
2986:
2984:
2981:
2979:
2976:
2974:
2971:
2967:
2964:
2962:
2961:by definition
2959:
2958:
2957:
2954:
2950:
2947:
2946:
2945:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2925:
2922:
2921:
2918:
2915:
2913:
2909:
2904:
2898:
2894:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2849:
2848:KripkeâPlatek
2846:
2844:
2841:
2837:
2834:
2832:
2829:
2828:
2827:
2824:
2823:
2821:
2817:
2809:
2806:
2805:
2804:
2801:
2799:
2796:
2792:
2789:
2788:
2787:
2784:
2782:
2779:
2777:
2774:
2772:
2769:
2767:
2764:
2761:
2757:
2753:
2750:
2746:
2743:
2741:
2738:
2736:
2733:
2732:
2731:
2727:
2724:
2723:
2721:
2719:
2715:
2711:
2703:
2700:
2698:
2695:
2693:
2692:constructible
2690:
2689:
2688:
2685:
2683:
2680:
2678:
2675:
2673:
2670:
2668:
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2648:
2645:
2643:
2640:
2638:
2635:
2633:
2630:
2628:
2625:
2624:
2622:
2620:
2615:
2607:
2604:
2602:
2599:
2597:
2594:
2592:
2589:
2587:
2584:
2582:
2579:
2578:
2576:
2572:
2569:
2567:
2564:
2563:
2562:
2559:
2557:
2554:
2552:
2549:
2547:
2544:
2542:
2538:
2534:
2532:
2529:
2525:
2522:
2521:
2520:
2517:
2516:
2513:
2510:
2508:
2504:
2494:
2491:
2489:
2486:
2484:
2481:
2479:
2476:
2474:
2471:
2469:
2466:
2462:
2459:
2458:
2457:
2454:
2450:
2445:
2444:
2443:
2440:
2439:
2437:
2435:
2431:
2423:
2420:
2418:
2415:
2413:
2410:
2409:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2374:
2372:
2370:
2369:Propositional
2366:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2328:
2325:
2324:
2323:
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2297:Logical truth
2295:
2293:
2290:
2289:
2287:
2285:
2281:
2278:
2276:
2272:
2266:
2263:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2237:
2233:
2229:
2227:
2224:
2222:
2219:
2217:
2213:
2210:
2209:
2207:
2205:
2199:
2194:
2188:
2185:
2183:
2180:
2178:
2175:
2173:
2170:
2168:
2165:
2163:
2160:
2158:
2155:
2153:
2150:
2148:
2145:
2143:
2140:
2138:
2135:
2133:
2130:
2126:
2123:
2122:
2121:
2118:
2117:
2115:
2111:
2107:
2100:
2095:
2093:
2088:
2086:
2081:
2080:
2077:
2070:
2069:3-540-90578-2
2066:
2062:
2061:
2056:
2055:
2054:
2039:
2035:
2031:
2027:
2020:
2012:
2005:
1997:
1990:
1982:
1976:
1972:
1965:
1957:
1951:
1947:
1946:
1938:
1930:
1924:
1920:
1915:
1914:
1905:
1897:
1891:
1887:
1886:
1878:
1870:
1864:
1860:
1859:
1854:
1848:
1844:
1833:
1830:
1828:
1825:
1822:
1819:
1816:
1813:
1811:
1809:
1805:
1803:
1801:
1797:
1795:
1792:
1790:
1787:
1785:
1783:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1757:
1754:
1752:
1749:
1748:
1743:
1732:
1729:
1723:
1718:
1711:
1709:
1705:
1702:
1698:
1694:
1690:
1686:
1681:
1679:
1675:
1671:
1667:
1663:
1659:
1654:
1652:
1648:
1647:chess variant
1643:
1641:
1638:means having
1637:
1633:
1625:
1621:
1618:
1615:
1612:
1610:
1607:
1606:
1603:
1601:
1598:
1595:
1592:
1591:
1588:
1586:
1583:
1580:
1577:
1576:
1573:
1571:
1568:
1565:
1562:
1561:
1558:
1556:
1553:
1550:
1547:
1546:
1543:
1541:
1538:
1535:
1532:
1531:
1528:
1526:
1523:
1520:
1517:
1516:
1513:
1511:
1508:
1505:
1502:
1501:
1498:
1496:
1493:
1490:
1487:
1486:
1483:
1480:
1478:
1475:
1472:
1470:
1467:
1464:
1463:
1459:
1455:
1451:
1447:
1445:
1442:
1439:
1437:
1434:
1431:
1430:
1426:
1422:
1420:
1417:
1414:
1412:
1409:
1406:
1405:
1402:
1398:
1394:
1392:
1388:
1385:
1382:
1378:
1375:
1374:
1370:
1367:
1364:
1361:
1358:
1355:
1354:
1351:
1349:
1345:
1341:
1337:
1333:
1329:
1325:
1321:
1312:
1310:
1309:
1304:
1303:
1295:Varying arity
1292:
1290:
1286:
1282:
1278:
1273:
1269:
1264:
1260:
1256:
1255:product space
1252:
1247:
1245:
1241:
1225:
1219:
1212:
1208:
1204:
1199:
1195:
1189:
1185:
1175:
1169:
1166:
1160:
1154:
1150:
1144:
1139:
1136:
1133:
1129:
1124:
1114:
1110:
1107:
1103:
1098:
1083:
1077:
1073:
1069:
1066:
1063:
1058:
1054:
1050:
1045:
1041:
1034:
1030:
1023:
1019:
1012:
1007:
1004:
1001:
997:
992:
986:
983:
978:
969:
958:
954:
950:
942:
937:
892:
888:
883:
881:
863:
853:
849:
836:
835:dc calculator
831:
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731:
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723:
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619:According to
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29:
22:
3814:
3612:Ultraproduct
3459:Model theory
3424:Independence
3360:Formal proof
3352:Proof theory
3335:
3308:
3265:real numbers
3237:second-order
3148:Substitution
3025:Metalanguage
2966:conservative
2939:Axiom schema
2928:
2883:Constructive
2853:MorseâKelley
2819:Set theories
2798:Aleph number
2791:inaccessible
2697:Grothendieck
2581:intersection
2468:Higher-order
2456:Second-order
2402:Truth tables
2359:Venn diagram
2142:Formal proof
2058:
2052:
2029:
2025:
2019:
2010:
2004:
1995:
1989:
1970:
1964:
1944:
1937:
1912:
1904:
1884:
1877:
1857:
1847:
1807:
1799:
1784:-adic number
1781:
1682:
1677:
1673:
1655:
1644:
1639:
1635:
1631:
1630:
1616:sum; e.g., ÎŁ
1380:
1356:
1347:
1343:
1339:
1327:
1318:
1306:
1300:
1298:
1274:
1267:
1258:
1250:
1248:
1243:
1238:Note that a
1112:
1105:
1099:
956:
952:
946:
940:
884:
832:
821:
753:
719:
705:
699:
693:
687:
661:
643:
641:
632:
628:
624:
618:
604:and in some
599:
525:Examples of
524:
511:hidden input
510:
507:side effects
500:
495:
489:
369:
365:
128:
126:
114:
106:
102:
39:
25:
3722:Type theory
3670:undecidable
3602:Truth value
3489:equivalence
3168:non-logical
2781:Enumeration
2771:Isomorphism
2718:cardinality
2702:Von Neumann
2667:Ultrafilter
2632:Uncountable
2566:equivalence
2483:Quantifiers
2473:Fixed-point
2442:First-order
2322:Consistency
2307:Proposition
2284:Traditional
2255:Lindström's
2245:Compactness
2187:Type theory
2132:Cardinality
1789:Cardinality
1689:syntactical
1315:Terminology
595:logical NOT
571:square root
531:unary minus
372:arguments.
141:hexadecimal
111:linguistics
85:taken by a
32:mathematics
3837:Categories
3533:elementary
3226:arithmetic
3094:Quantifier
3072:functional
2944:Expression
2662:Transitive
2606:identities
2591:complement
2524:hereditary
2507:Set theory
1839:References
1810:-ary group
1653:of 1603).
1539:hebdomadic
1491:quaternary
1460:operators
1308:multigrade
1279:such as a
1246:arguments
593:, and the
547:reciprocal
513:, such as
135:, such as
99:philosophy
3804:Supertask
3707:Recursion
3665:decidable
3499:saturated
3477:of models
3400:deductive
3395:axiomatic
3315:Hilbert's
3302:Euclidean
3283:canonical
3206:axiomatic
3138:Signature
3067:Predicate
2956:Extension
2878:Ackermann
2803:Operation
2682:Universal
2672:Recursive
2647:Singleton
2642:Inhabited
2627:Countable
2617:Types of
2601:power set
2571:partition
2488:Predicate
2434:Predicate
2349:Syllogism
2339:Soundness
2312:Inference
2302:Tautology
2204:paradoxes
1802:-ary code
1776:Parameter
1697:functions
1693:operators
1662:predicate
1536:septenary
1427:operator
1348:singulary
1240:logarithm
1205:⋯
1130:∏
1067:⋯
998:∑
973:¯
833:The Unix
676:logarithm
543:factorial
539:successor
441:∏
415:…
375:Example:
304:Example:
246:Example:
197:Example:
154:Example:
91:operation
79:arguments
3789:Logicism
3782:timeline
3758:Concrete
3617:Validity
3587:T-schema
3580:Kripke's
3575:Tarski's
3570:semantic
3560:Strength
3509:submodel
3504:spectrum
3472:function
3320:Tarski's
3309:Elements
3296:geometry
3252:Robinson
3173:variable
3158:function
3131:spectrum
3121:Sentence
3077:variable
3020:Language
2973:Relation
2934:Automata
2924:Alphabet
2908:language
2762:-jection
2740:codomain
2726:Function
2687:Universe
2657:Infinite
2561:Relation
2344:Validity
2334:Argument
2232:theorem,
1855:(2001).
1832:Finitary
1714:See also
1658:relation
1613:variadic
1599:polyadic
1569:enneadic
1554:ogdoadic
1551:octonary
1509:pentadic
1494:tetradic
1448:logical
1444:addition
1423:logical
1391:constant
1320:Latinate
1302:variadic
1289:currying
684:division
680:addition
492:constant
123:Examples
95:relation
87:function
83:operands
3731:Related
3528:Diagram
3426: (
3405:Hilbert
3390:Systems
3385:Theorem
3263:of the
3208:systems
2988:Formula
2983:Grammar
2899: (
2843:General
2556:Forcing
2541:Element
2461:Monadic
2236:paradox
2177:Theorem
2113:General
1608:varying
1584:decadic
1524:hexadic
1506:quinary
1473:triadic
1469:ternary
1415:monadic
1386:niladic
1344:singulī
716:Ternary
644:monadic
625:singuli
616:below.
555:ceiling
486:Nullary
131:-based
116:valency
103:adicity
21:Acidity
3494:finite
3257:Skolem
3210:
3185:Theory
3153:Symbol
3143:String
3126:atomic
3003:ground
2998:closed
2993:atomic
2949:ground
2912:syntax
2808:binary
2735:domain
2652:Finite
2417:finite
2275:Logics
2234:
2182:Theory
2067:
1977:
1952:
1925:
1892:
1865:
1666:domain
1624:reduce
1578:10-ary
1521:senary
1440:dyadic
1436:binary
1381:nƫllus
1179:
1111:is an
885:Many (
778:Elixir
756:Python
664:binary
658:Binary
137:binary
107:degree
34:, and
3484:Model
3232:Peano
3089:Proof
2929:Arity
2858:Naive
2745:image
2677:Fuzzy
2637:Empty
2586:union
2531:Class
2172:Model
2162:Lemma
2120:Axiom
1563:9-ary
1548:8-ary
1533:7-ary
1518:6-ary
1503:5-ary
1488:4-ary
1465:3-ary
1432:2-ary
1411:unary
1407:1-ary
1401:False
1376:0-ary
1287:, by
1281:tuple
878:with
824:Forth
776:. In
738:Julia
633:terni
621:Quine
614:n-ary
551:floor
521:Unary
145:Latin
109:. In
67:
40:arity
28:logic
3607:Type
3410:list
3214:list
3191:list
3180:Term
3114:rank
3008:open
2902:list
2714:Maps
2619:sets
2478:Free
2448:list
2198:list
2125:list
2065:ISBN
2026:Mind
1975:ISBN
1950:ISBN
1923:ISBN
1890:ISBN
1863:ISBN
1695:and
1660:(or
1397:True
1359:-ary
1340:unus
947:The
943:-ary
932:and
887:RISC
822:The
807:else
770:else
754:The
742:Perl
734:Java
710:CISC
629:bini
583:norm
563:sign
143:. A
139:and
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3294:of
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2730:Map
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1270:â 1
1104:of
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896:MOV
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726:C++
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689:OR
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