U matematici povsyakchas vikoristovuyutsya simvoli dlya sproshennya ta skorochennya vikladennya Nizhche navedeno spisok matematichnih simvoliv sho zustrichayutsya najchastishe Najposhirenishi Plyus Minus Znak mnozhennya Znak dilennya Simvol pidnesennya do stepenya Znak rivnosti Znak kongruentnosti Znaki porivnyannya lt gt Znak poryadku tilda Znak plyus minus Znak korenya Faktorial Znak integralu displaystyle int Simvol TeX Simvol Unicode Nazva Znachennya PrikladVimovaRozdil matematiki displaystyle Rightarrow Implikaciya sliduvannya A B displaystyle A Rightarrow B oznachaye koli A displaystyle A istinne to B displaystyle B takozh istinne Inodi vikoristovuyut displaystyle rightarrow x 2 x 2 4 displaystyle x 2 Rightarrow x 2 4 istinne ale x 2 4 x 2 displaystyle x 2 4 Rightarrow x 2 hibno tomu sho x 2 displaystyle x 2 takozh ye rozv yazkom z viplivaye abo yaksho to skriz displaystyle Leftrightarrow Rivnosilnist A B displaystyle A Leftrightarrow B oznachaye A displaystyle A istinne todi i tilki todi koli B displaystyle B istinne x 5 y 2 x 3 y displaystyle x 5 y 2 Leftrightarrow x 3 y todi i tilki todi abo rivnosilno skriz displaystyle wedge Kon yunkciya A B displaystyle A wedge B istinne todi i tilki todi koli A displaystyle A i B displaystyle B obidva istini n gt 2 n lt 4 n 3 displaystyle n gt 2 wedge n lt 4 Leftrightarrow n 3 yaksho n displaystyle n naturalne chislo i Matematichna logika displaystyle vee Diz yunkciya A B displaystyle A vee B istinne koli hocha b odna z umov A displaystyle A abo B displaystyle B ye istinnoyu n 2 n 4 n 3 displaystyle n leqslant 2 vee n geqslant 4 Leftrightarrow n neq 3 yaksho n displaystyle n naturalne chislo abo Matematichna logika displaystyle neg Zaperechennya A displaystyle neg A istinne todi i tilki todi koli hibno A displaystyle A A B A B displaystyle neg A wedge B Leftrightarrow neg A vee neg B x S x S displaystyle x notin S Leftrightarrow neg x in S ne Matematichna logika displaystyle forall Kvantor zagalnosti x P x displaystyle forall x P x oznachaye P x displaystyle P x istinne dlya vsih x displaystyle x n N n 2 n displaystyle forall n in mathbb N n 2 geqslant n Dlya bud yakih Dlya vsih Matematichna logika displaystyle exists Kvantor isnuvannya x P x displaystyle exists x P x oznachaye isnuye hocha b odne x displaystyle x take sho P x displaystyle P x istinne n N n 5 2 n displaystyle exists n in mathbb N n 5 2n pidhodit chislo 5 isnuye Matematichna logika displaystyle Rivnist x y displaystyle x y oznachaye x displaystyle x i y displaystyle y oznachayut odin i toj zhe ob yekt 1 2 6 3 dorivnyuye skriz displaystyle displaystyle Leftrightarrow d e f displaystyle stackrel rm def Viznachennya x y displaystyle x y oznachaye x displaystyle x za viznachennyam dorivnyuye y displaystyle y P Q displaystyle P Leftrightarrow Q oznachaye P displaystyle P za viznachennyam rivnosilno Q displaystyle Q c h x 1 2 e x e x displaystyle rm ch x 1 over 2 left e x e x right Giperbolichnij kosinus A B A B A B displaystyle A oplus B Leftrightarrow A vee B wedge neg A wedge B Viklyuchayuche abo dorivnyuye rivnosilno za viznachennyam skriz displaystyle Mnozhina elementiv a b c displaystyle a b c oznachaye mnozhina elementami yakoyi ye a displaystyle a b displaystyle b ta c displaystyle c N 0 1 2 displaystyle mathbb N 0 1 2 ldots mnozhina naturalnih chisel Mnozhina Teoriya mnozhin displaystyle displaystyle Mnozhina elementiv sho zadovolnyayut umovi x P x displaystyle x P x oznachaye mnozhinu usih x displaystyle x takih sho istinne P x displaystyle P x n N n 2 lt 20 1 2 3 4 displaystyle n in mathbb N n 2 lt 20 1 2 3 4 Mnozhina vsih takih sho istinne Teoriya mnozhin displaystyle varnothing displaystyle Porozhnya mnozhina displaystyle i displaystyle varnothing oznachaye mnozhinu sho ne mistit zhodnogo elementu n N 1 lt n 2 lt 4 displaystyle n in mathbb N 1 lt n 2 lt 4 varnothing Porozhnya mnozhina Teoriya mnozhin displaystyle in displaystyle notin prinalezhnist neprinalezhnist do mnozhini a S displaystyle a in S oznachaye a displaystyle a ye elementom mnozhini S displaystyle S a S displaystyle a notin S oznachaye a displaystyle a ne ye elementom S displaystyle S 2 N displaystyle 2 in mathbb N 1 2 N displaystyle 1 over 2 notin mathbb N nalezhit z ne nalezhit Teoriya mnozhin displaystyle subseteq displaystyle subset Pidmnozhina A B displaystyle A subseteq B oznachaye kozhnij element z A displaystyle A takozh ye elementom z B displaystyle B A B displaystyle A subset B yak pravilo oznachaye te zh sho i A B displaystyle A subseteq B Odnak deyaki avtori vikoristovuyut displaystyle subset shob pokazati stroge vklyuchennya a same displaystyle subsetneq A B A displaystyle A cap B subseteq A Q R displaystyle mathbb Q subseteq mathbb R ye pidmnozhinoyu vklyucheno v Teoriya mnozhin displaystyle subsetneq Vlasna pidmnozhina A B displaystyle A subsetneq B oznachaye A B displaystyle A subseteq B i A B displaystyle A neq B N Q displaystyle mathbb N subsetneq mathbb Q ye vlasnoyu pidmnozhinoyu strogo vklyuchayetsya v Teoriya mnozhin displaystyle cup Ob yednannya A B displaystyle A cup B oznachaye mnozhinu elementiv sho nalezhat A displaystyle A abo B displaystyle B abo obom odrazu A B A B B displaystyle A subseteq B Leftrightarrow A cup B B Ob yednannya i ob yednane z Teoriya mnozhin displaystyle cap Peretin A B displaystyle A cap B oznachaye mnozhinu elementiv sho nalezhat i A displaystyle A i B displaystyle B x R x 2 1 N 1 displaystyle x in mathbb R x 2 1 cap mathbb N 1 Peretin i peretnute z Teoriya mnozhin displaystyle setminus Riznicya mnozhin A B displaystyle A setminus B oznachaye mnozhinu elementiv sho nalezhat A displaystyle A ale ne nalezhat B displaystyle B 1 2 3 4 3 4 5 6 1 2 displaystyle 1 2 3 4 setminus 3 4 5 6 1 2 riznicya i minus bez Teoriya mnozhin displaystyle to Funkciya f X Y displaystyle f X to Y oznachaye funkciyu f displaystyle f sho vidobrazhaye mnozhinu oblast viznachennya X displaystyle X u mnozhinu Y displaystyle Y Funkciya f Z Z displaystyle f mathbb Z to mathbb Z sho viznachennya yak f x x 2 displaystyle f x x 2 z v skriz displaystyle mapsto Vidobrazhennya x f x displaystyle x mapsto f x oznachaye sho obrazom x displaystyle x pislya zastosuvannya funkciyi f displaystyle f bude f x displaystyle f x Funkciyu sho viznachennya yak f x x 2 displaystyle f x x 2 mozhna zapisati tak f x x 2 displaystyle f colon x mapsto x 2 vidobrazhuyetsya v skrizN displaystyle mathbb N N abo ℕ Naturalni chisla N displaystyle mathbb N oznachaye mnozhinu 1 2 3 displaystyle 1 2 3 ldots abo 0 1 2 3 displaystyle 0 1 2 3 ldots v zalezhnosti vid situaciyi a a Z N displaystyle left a right a in mathbb Z mathbb N En ChislaZ displaystyle mathbb Z Z abo ℤ Cili chisla Z displaystyle mathbb Z oznachaye mnozhinu 3 2 1 0 1 2 3 displaystyle ldots 3 2 1 0 1 2 3 ldots a a a N Z displaystyle a a a in mathbb N mathbb Z Zet ChislaQ displaystyle mathbb Q Q abo ℚ Racionalni chisla Q displaystyle mathbb Q oznachaye p q p Z q Z q 0 displaystyle left left p over q right p in mathbb Z wedge q in mathbb Z wedge q neq 0 right 3 14 Q displaystyle 3 14 in mathbb Q p Q displaystyle pi notin mathbb Q Ku ChislaR displaystyle mathbb R R abo ℝ Realni chisla abo dijsni chisla R displaystyle mathbb R oznachaye mnozhinu vsih mezh poslidovnostej z Q displaystyle mathbb Q p R displaystyle pi in mathbb R i R displaystyle i notin mathbb R i displaystyle i kompleksne chislo i 2 1 displaystyle i 2 1 Er ChislaC displaystyle mathbb C C abo ℂ Kompleksni chisla C displaystyle mathbb C oznachaye mnozhinu a b i a R b R displaystyle a b cdot i a in mathbb R wedge b in mathbb R i C displaystyle i in mathbb C Ce Chisla lt displaystyle lt gt displaystyle gt lt gt Porivnyannya x lt y displaystyle x lt y oznachaye sho x displaystyle x ye strogo menshim vid y displaystyle y x gt y displaystyle x gt y oznachaye sho x displaystyle x ye strogo bilshim vid y displaystyle y x lt y y gt x displaystyle x lt y Leftrightarrow y gt x menshe nizh bilshe nizh Vidnoshennya poryadku displaystyle leqslant displaystyle geqslant abo abo Porivnyannya x y displaystyle x leqslant y oznachaye sho x displaystyle x ye menshim abo dorivnyuye y displaystyle y x y displaystyle x geqslant y oznachaye sho x displaystyle x ye bilshim abo dorivnyuye y displaystyle y x 1 x 2 x displaystyle x geqslant 1 Rightarrow x 2 geqslant x menshe abo dorivnyuye bilshe abo dorivnyuye Vidnoshennya poryadku displaystyle approx Priblizna rivnist e 2 718 displaystyle e approx 2 718 z tochnistyu do 10 3 displaystyle 10 3 oznachaye sho 2 718 vidriznyayetsya vid e displaystyle e ne bilshe nizh na 10 3 displaystyle 10 3 p 3 1415926 displaystyle pi approx 3 1415926 z tochnistyu do 10 7 displaystyle 10 7 priblizno dorivnyuye Chisla displaystyle sqrt Arifmetichnij kvadratnij korin x displaystyle sqrt x oznachaye dodatne dijsne chislo yake v kvadrati daye x displaystyle x 4 2 displaystyle sqrt 4 2 x 2 x displaystyle sqrt x 2 left x right Korin kvadratnij z Chisla displaystyle infty Neskinchennist displaystyle infty ta displaystyle infty sut elementi rozshirenoyi mnozhini dijsnih chisel Ci simvoli poznachayut chisla sho ye menshimi bilshimi vid usih dijsnih chisel lim x 0 1 x displaystyle lim limits x to 0 1 over left x right infty Plyus minus neskinchennist Chisla displaystyle left right Modul chisla absolyutne znachennya modul kompleksnogo chisla abo potuzhnist mnozhini x displaystyle left x right oznachaye absolyutnu velichinu x displaystyle x A displaystyle A oznachaye potuzhnist mnozhini A displaystyle A ta dorivnyuye yaksho A displaystyle A skinchenna chislu elementiv A displaystyle A a b i a 2 b 2 displaystyle left a b cdot i right sqrt a 2 b 2 Modul Potuzhnist Chisla i Teoriya mnozhin displaystyle sum Suma suma ryadu k 1 n a k displaystyle sum k 1 n a k oznachaye suma a k displaystyle a k de k displaystyle k prijmaye znachennya vid 1 do n displaystyle n a same a 1 a 2 a n displaystyle a 1 a 2 ldots a n k 1 a k displaystyle sum k 1 infty a k oznachaye sumu ryadu sho skladayetsya z a k displaystyle a k k 1 4 k 2 displaystyle sum k 1 4 k 2 1 2 2 2 3 2 4 2 displaystyle 1 2 2 2 3 2 4 2 30 displaystyle 30 Suma po vid do Arifmetika Matematichnij analiz displaystyle prod Dobutok k 1 n a k displaystyle prod k 1 n a k oznachaye dobutok a k displaystyle a k dlya usih k displaystyle k vid 1 do n displaystyle n a same a 1 a 2 a n displaystyle a 1 cdot a 2 cdot ldots cdot a n k 1 4 k 2 displaystyle prod k 1 4 k 2 3 4 5 6 360 displaystyle 3 cdot 4 cdot 5 cdot 6 360 Dobutok po vid do Arifmetika d x displaystyle int dx Integral a b f x d x displaystyle int limits a b f x dx oznachaye Integral vid a displaystyle a do b displaystyle b funkciyi f displaystyle f vid x displaystyle x po zminnij x displaystyle x 0 b x 2 d x b 3 3 displaystyle int limits 0 b x 2 dx b 3 3 x 2 d x x 3 3 displaystyle int x 2 dx x 3 3 Integral vid do funkciyi po Matematichnij analizd f d x displaystyle frac df dx f x displaystyle f x df dx f x Pohidna d f d x displaystyle frac df dx abo f x displaystyle f x oznachaye persha pohidna funkciyi f displaystyle f vid x displaystyle x po zminnij x displaystyle x d cos x d x sin x displaystyle frac d cos x dx sin x Pohidna po Matematichnij analizd n f d x n displaystyle frac d n f dx n f n x displaystyle f n x d n f d x n displaystyle d n f dx n f n x displaystyle f n x Pohidna n displaystyle n go poryadku d n f d x n displaystyle frac d n f dx n abo f n x displaystyle f n x v drugomu vipadku yaksho n displaystyle n fiksovane chislo to vono pishetsya rimskimi ciframi oznachaye n displaystyle n ya pohidna funkciyi f displaystyle f vid x displaystyle x po zminnij x displaystyle x d 4 cos x d x 4 cos x displaystyle frac d 4 cos x dx 4 cos x n displaystyle n ya pohidna po Matematichnij analizDiv takozh RedaguvatiTablicya poznachen abstraktnoyi algebri Istoriya matematichnih poznachen Spisok poznachen u fizici Dovidka Matematichni formuli ta specsimvoli pravila redaguvannya matematichnih formul na Vikipediyi Otrimano z https uk wikipedia org w index php title Tablicya matematichnih simvoliv amp oldid 36753248
