கணிதக் குறியீடுகள்

கணித தகவல்களை வெளிப்படுத்த கணிதக் குறியீடுகள் பயன்படுகின்றன.  எழுத்துக்கள் எப்படி மொழியூடாக தகவல்களை வெளிப்படுத்த அவசியமோ அதேபோல் குறியீடுகள் கணிதத்தினூடாக தகவல்களை வெளிப்படுத்த அவசியம்.  ஒரு மொழியை அறிய, பயன்படுத்த எப்படி அதன் எழுத்துக்களை அறிவது அவசியமோ அதேபோல் கணிதத்தை அறிய, பயன்படுத்த கணிதக் குறியீடுகளை அறிவது அவசியம்.  எண்கள், செயற்பாட்டுக் குறியீடுகள், கருத்துருக் குறியீடுகள், சமன்பாடுகள் என பலநிலையிலான குறியீடுகள் கணிதத்தில் உண்டு.

 அடிப்படை கணிதக் குறியீடுகள் அட்டவணை 

குறியீடுபெயர்விளக்கம்எடுத்துக்காட்டு பலுக்கும் முறைபகுப்பு=சமம்காட்டாக 2 + 3 = 5 என்பது ஒரு சமன்பாடு. இதனை 2 கூட்டல் 3 ஈடு 5 என்று படிக்கலாம், அல்லது 2 கூட்டல் 3 சமம் 5 என்று படிக்கலாம். அதே போல 2 + 4 = 3 x 2 என்பதும் ஒரு சமன்பாடு.1 + 1 = 2சமமாக, ஈடாகஎங்கும்≠<>!=சமனிலி x ≠ y என்பது x ம் y யும் ஒன்றல்ல, ஒரே மதிப்பைக் கொள்ளவில்லை.  .(குறியீடுகள் != ம் <>  கணினியியலில் பயன்படுகிறது.)
| rowspan=3|1 ≠ 2
|-
|align=center|சமமில்லை
|-
|align=right valign=center|

|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<>≪≫
||strict inequality
| rowspan=3|x < y என்பது x ஐவிடச் சிறியது y. x > y என்பது x yயிலும் பெரியது.  x ≪ y என்பது x y ஐவிட மிகச் சிறியது.x ≫ y என்பது x yஐவிடப் மிகவும் பெரியது.
| rowspan=3|3 < 4  5 > 4.
0.003 ≪ 1000000
|-
|align=center|is less than, is greater than, is much less than, is much greater than
|-
|align=right|order theory

|-
| rowspan=3 bgcolor=#d0f0d0 align=center|≤<=≥>=
||inequality
| rowspan=3|x ≤ y means x is less than or equal to y.x ≥ y means x is greater than or equal to y.(The symbols <= and >= are primarily from computer science. They are avoided in mathematical texts.)
| rowspan=3|3 ≤ 4 and 5 ≤ 5 5 ≥ 4 and 5 ≥ 5
|-
|align=center|is less than or equal to, is greater than or equal to
|-
|align=right|order theory

|-
| rowspan=3 bgcolor=#d0f0d0 align=center|∝
||proportionality
| rowspan=3| y ∝ x means that y = kx for some constant k.
| rowspan=3|if y = 2x, then y ∝ x|-
|align=center|is proportional to; varies as
|-
|align=right valign=center|everywhere

|-
| rowspan=6 bgcolor=#d0f0d0 align=center|+
|கூட்டல்
| rowspan=3|4 + 6 means the sum of 4 and 6.
| rowspan=3|2 + 7 = 9
|-
|align=center|plus
|-
|align=right|எண்கணிதம்

|-
| disjoint union
| rowspan=3|A1 + A2 means the disjoint union of sets A1 and A2.
| rowspan=3|A1 = {1, 2, 3, 4} ∧ A2 = {2, 4, 5, 7} ⇒ A1 + A2 = {(1,1), (2,1), (3,1), (4,1), (2,2), (4,2), (5,2), (7,2)}
|-
|align=center|the disjoint union of … and …
|-
|align=right|set theory

|-
| rowspan=9 bgcolor=#d0f0d0 align=center|−
|கழித்தல்
| rowspan=3|9 − 4 means the subtraction of 4 from 9.
| rowspan=3|8 − 3 = 5
|-
|align=center|minus
|-
|align=right|எண்கணிதம்
|-

|negative sign
| rowspan=3|−3 means the negative of the number 3.
| rowspan=3|−(−5) = 5
|-
|align=center|negative; minus
|-
|align=right|எண்கணிதம்
|-

|set-theoretic complement
| rowspan=3|A − B means the set that contains all the elements of A that are not in B.  ∖ can also be used for set-theoretic complement as described below.
| rowspan=3|{1,2,4} − {1,3,4}  =  {2}
|-
|align=center|minus; without
|-
|align=right|set theory

|-
| rowspan=9 bgcolor=#d0f0d0 align=center|×
|பெருக்கல்
| rowspan=3|3 × 4 means the multiplication of 3 by 4.
| rowspan=3|7 × 8 = 56
|-
|align=center|times
|-
|align=right|எண்கணிதம்

|-
|கார்ட்டீசியன் பெருக்கற்பலன்
| rowspan=3|X×Y means the set of all வரிசைச் சோடி with the first element of each pair selected from X and the second element selected from Y.
| rowspan=3|{1,2} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}
|-
|align=center|the Cartesian product of … and ...; the direct product of … and …
|-
|align=right|set theory

|-
|குறுக்குப் பெருக்கு
| rowspan=3|u × v means the cross product of vectors u and v
| rowspan=3|(1,2,5) × (3,4,−1) = (−22, 16, − 2)
|-
|align=center|cross
|-
|align=right|vector algebra

|-
| rowspan=6 bgcolor=#d0f0d0 align=center|·
|பெருக்கல்
| rowspan=3|3 · 4 means the multiplication of 3 by 4.
| rowspan=3|7 · 8 = 56
|-
|align=center|times
|-
|align=right|எண்கணிதம்

|-
|புள்ளிப் பெருக்கல்
| rowspan=3|u · v means the dot product of vectors u and v
| rowspan=3|(1,2,5) · (3,4,−1) = 6
|-
|align=center|dot
|-
|align=right|vector algebra

|-
| rowspan=3 bgcolor=#d0f0d0 align=center|÷ ⁄
||division
| rowspan=3|6 ÷ 3 or 6 ⁄ 3 means the division of 6 by 3.
| rowspan=3|2 ÷ 4 = .5 12 ⁄ 4 = 3
|-
|align=center|divided by
|-
|align=right|எண்கணிதம்

|-
| rowspan=6 bgcolor=#d0f0d0 align=center|±
||plus-minus
| rowspan=3|6 ± 3 means both 6 + 3 and 6 – 3.
| rowspan=3|The equation x = 5 ± √4, has two solutions, x = 7 and x = 3.
|-
|align=center|plus or minus
|-
|align=right|எண்கணிதம்
|-
||plus-minus
| rowspan=3|10 ± 2 or equivalently 10 ± 20%  means the range from 10 − 2 to 10 + 2.
| rowspan=3| If a = 100 ± 1 mm, then a ≥ 99 mm and a ≤ 101 mm. 
|-
|align=center|plus or minus
|-
|align=right|அளவியல்

|-
| rowspan=3 bgcolor=#d0f0d0 align=center|
||minus-plus
| rowspan=3|6 ± (3  5) means both 6 + (3 – 5) and 6 – (3 + 5).
| rowspan=3|cos(x ± y) = cos(x) cos(y)  sin(x) sin(y).
|-
|align=center|minus or plus
|-
|align=right|எண்கணிதம்

|-
| rowspan=6 bgcolor=#d0f0d0 align=center|√
||வர்க்கமூலம்
| rowspan=3|√x means the positive number whose square is x.
| rowspan=3|√4 = 2
|-
|align=center|the principal square root of; square root
|-
|align=right|மெய்யெண்

|-
||complex square root
| rowspan=3| if z = r exp(iφ) is represented in polar coordinates with -π < φ ≤ π, then √z = √r exp(i φ/2).
| rowspan=3|√(-1) = i|-
|align=center|the complex square root of … square root
|-
|align=right|சிக்கலெண்

|-
| rowspan=9 bgcolor=#d0f0d0 align=center||…|
||தனி மதிப்பு or modulus
| rowspan=3| |x| means the distance along the real line (or across the complex plane) between x and zero.
| rowspan=3| |3| = 3 |–5| = |5| | i | = 1 | 3 + 4i | = 5
|-
|align=center|absolute value (modulus) of
|-
|align=right|எண்s

|-
||யூக்ளிடிய தொலைவு
| rowspan=3| |x – y| means the Euclidean distance between x and y.
| rowspan=3| For x = (1,1), and y = (4,5),  |x – y| = √([1–4]2 + [1–5]2) = 5
|-
|align=center|Euclidean distance between; Euclidean norm of
|-
|align=right|வடிவவியல்

|-
||அணிக்கோவை
| rowspan=3| |A| means the determinant of the matrix A
| rowspan=3| 
|-
|align=center|determinant of
|-
|align=right|அணி (கணிதம்)

|-
| rowspan=3 bgcolor=#d0f0d0 align=center||
||divides
| rowspan=3| A single vertical bar is used to denote divisibility. a|b means a divides b.
| rowspan=3| Since 15 = 3×5, it is true that 3|15 and 5|15.
|-
|align=center|divides
|-
|align=right|Number Theory

|-
| rowspan=3 bgcolor=#d0f0d0 align=center|!
||தொடர் பெருக்கம்
| rowspan=3|n ! is the product 1 × 2× … × n.
| rowspan=3|4! = 1 × 2 × 3 × 4 = 24
|-
|align=center|factorial
|-
|align=right|சேர்வியல் (கணிதம்)
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|T
||transpose
| rowspan=3| Swap rows for columns
| rowspan=3| 
|-
|align=center|transpose
|-
|align=right|அணி (கணிதம்)s
|-
| rowspan=6 bgcolor=#d0f0d0 align=center|~
||நிகழ்தகவுப் பரவல்
| rowspan=3| X ~ D, means the சமவாய்ப்பு மாறி X has the probability distribution D.
| rowspan=3|X ~ N(0,1), the இயல்நிலைப் பரவல்has distributionபுள்ளியியல்Row equivalence A~B means that B can be generated by using a series of elementary row operations on A is row equivalent toஅணி (கணிதம்)⇒ → ⊃material implicationA ⇒ B means if A is true then B is also true; if A is false then nothing is said about B. → may mean the same as ⇒, or it may have the meaning for functions given below. ⊃ may mean the same as ⇒, or it may have the meaning for superset given below.x = 2  ⇒  x2 = 4 is true, but x2 = 4   ⇒  x = 2 is in general false (since x could be −2).implies; if … thenpropositional logic, Heyting algebra⇔ ↔material equivalenceA ⇔ B means A is true if B is true and A is false if B is false.x + 5 = y +2  ⇔  x + 3 = yif and only if; iffpropositional logic¬ ˜logical negationThe statement ¬A is true if and only if A is false. A slash placed through another operator is the same as "¬" placed in front.(The symbol ~ has many other uses, so ¬  or the slash notation is preferred.)¬(¬A) ⇔ A  x ≠ y  ⇔  ¬(x =  y)notpropositional logic∧logical conjunction or meet in a latticeThe statement A ∧ B is true if A and B are both true; else it is false. For functions A(x) and B(x), A(x) ∧ B(x) is used to mean min(A(x), B(x)).n < 4  ∧  n >2  ⇔  n = 3 when n is a இயல் எண்.and; minpropositional logic, lattice theory∨logical disjunction or join in a latticeThe statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false.  For functions A(x) and B(x), A(x) ∨ B(x) is used to mean max(A(x), B(x)).n ≥ 4  ∨  n ≤ 2  ⇔ n ≠ 3 when n is a இயல் எண்.or; maxpropositional logic, lattice theory⊕  exclusive or The statement A ⊕ B is true when either A or B, but not both, are true. A  B means the same. (¬A) ⊕ A is always true, A ⊕ A is always false.xorpropositional logic, Boolean algebradirect sumThe direct sum is a special way of combining several modules into one general module (the symbol ⊕ is used,  is only for logic).Most commonly, for vector spaces U, V, and W, the following consequence is used: U = V ⊕ W ⇔ (U = V + W) ∧ (V ∩ W = )direct sum ofAbstract algebra∀universal quantification∀ x: P(x) means P(x) is true for all x.∀ n ∈ : n2 ≥ n.for all; for any; for eachpredicate logic∃existential quantification∃ x: P(x) means there is at least one x such that P(x) is true.∃ n ∈ : n is even.there existspredicate logic∃!uniqueness quantification∃! x: P(x) means there is exactly one x such that P(x) is true.∃! n ∈ : n + 5 = 2n.there exists exactly onepredicate logic:=≡:⇔வரைவிலக்கணம்x := y or x ≡ y means x is defined to be another name for y(Some writers use ≡ to mean congruence). P :⇔ Q means P is defined to be logically equivalent to Q.cosh x := (1/2)(exp x +  exp (−x)) A xor B :⇔ (A ∨ B) ∧ ¬(A ∧ B)is defined aseverywherecongruence△ABC  △DEF means triangle ABC is congruent to (has the same measurements as) triangle DEF.is congruent toவடிவவியல்≡congruence relationa ≡ b (mod n) means a − b is divisible by n5 ≡ 11 (mod 3)… is congruent to … modulo …சமானம், மாடுலோ n{ , }தொடை brackets{a,b,c} means the set consisting of a, b, and c. = { 1, 2, 3, …}the set of …set theory{ : } { | }set builder notation{x : P(x)} means the set of all x for which P(x) is true. {x | P(x)} is the same as {x : P(x)}.{n ∈  : n2 < 20} = { 1, 2, 3, 4}the set of … such thatset theory{ } சூனியத்தொடை means the set with no elements. { } means the same.{n ∈  : 1 < n2 < 4} =  the empty setset theory∈set membershipa ∈ S என்பது a , Sதொடையின் மூலகமாகும் ; a  S என்பது  a ,Sதொடையின் மூலகமல்ல என்றும் குறித்து நிற்கும் .(1/2)−1 ∈  2−1  மூலகம் ; மூலகமன்றுeverywhere, set theory⊆⊂உபதொடை(subset) A ⊆ B means every element of A is also element of B. (proper subset) A ⊂ B means A ⊆ B but A ≠ B. (Some writers use the symbol ⊂ as if it were the same as ⊆.)(A ∩ B) ⊆ A ⊂  ⊂ is a subset ofset theory⊇ ⊃supersetA ⊇ B means every element of B is also element of A.A ⊃ B means A ⊇ B but A ≠ B. (Some writers use the symbol ⊃ as if it were the same as ⊇.)(A ∪ B) ⊇ B ⊃ is a superset ofset theory∪set-theoretic union(exclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, but not both. "A or B, but not both."  (inclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, or all the elements from both A and B. "A or B or both".A ⊆ B  ⇔  (A ∪ B) = B (inclusive)the union of … and …  unionset theory∩set-theoretic intersectionA ∩ B means the set that contains all  those elements that A and B have in common.{x ∈  : x2 = 1} ∩  = {1}intersected with; intersectset theory  symmetric difference means the set of elements in exactly one of A or B.{1,5,6,8}  {2,5,8} = {1,2,6}symmetric differenceset theoryset-theoretic complementA  B means the set that contains all those elements of A that are not in B. − can also be used for set-theoretic complement as described above.{1,2,3,4}  {3,4,5,6} = {1,2}minus; withoutset theory( )function applicationf(x) means the value of the function f at the element x.If f(x) := x2, then f(3) = 32 = 9.ofset theoryprecedence groupingPerform the operations inside the parentheses first.(8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.parentheseseverywheref:X→Yfunction arrowf: X → Y means the function f maps the set X into the set Y.Let f:  →  be defined by f(x) := x2.from … toset theory,type theoryoசார்புகளின் தொகுப்புfog is the function, such that (fog)(x) = f(g(x)).if f(x) := 2x, and g(x) := x + 3, then  (fog)(x) = 2(x + 3).composed withset theoryNஇயற்கை எண்கள்N means { 1, 2, 3, …}, but see the article on natural numbers for a different convention. = {|a| : a ∈ , a ≠ 0}Nஎண்sZ நிறை எண்கள் means {..., −3, −2, −1, 0, 1, 2, 3, …} and + means {1, 2, 3, …} = . = {p, -p : p ∈ } ∪ {0}Zஎண்s Q விகிதமுறு எண்கள் means {p/q : p ∈ , q ∈ }.3.14000... ∈ π  Qஎண்s R மெய்யெண்sℝ means the set of real numbers.π ∈  √(−1)  Rஎண்sC சிக்கலெண்s means {a + b i : a,b ∈ }.i = √(−1) ∈ Cஎண்sarbitrary constant C can be any number, most likely unknown; usually occurs when calculating antiderivatives.if f(x) = 6x² + 4x, then F(x) = 2x³ + 2x² + C, where F'(x) = f(x)CதொகையீடுKreal or சிக்கலெண்sK means the statement holds substituting K for R and also for C. 
because

and
.Kநேரியல் இயற்கணிதம்∞எண்ணிலி∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits.எண்ணிலிஎண்s||…||norm || x || is the norm of the element x of a normed vector space. || x  + y || ≤  || x ||  +   || y ||norm of length of நேரியல் இயற்கணிதம்∑summation means a1 + a2 + … + an. = 12 + 22 + 32 + 42 
= 1 + 4 + 9 + 16 = 30sum over … from … to … ofஎண்கணிதம்∏product means a1a2···an. = (1+2)(2+2)(3+2)(4+2)
= 3 × 4 ×  5 × 6 = 360product over … from … to … ofஎண்கணிதம்கார்ட்டீசியன் பெருக்கற்பலன் means the set of all (n+1)-tuples
(y0, …, yn).the Cartesian product of; the direct product ofset theorycoproductcoproduct over … from … to … ofcategory theory′  •வகையிடல்f ′(x) is the derivative of the function f at the point x, i.e., the சாய்வு of the தொடுகோடு to f at x. 
The dot notation indicates a time derivative. That is .If f(x) := x2, then f ′(x) = 2x… prime derivative ofநுண்கணிதம்∫indefinite integral or antiderivative∫ f(x) dx means a function whose derivative is f. ∫x2 dx = x3/3 + Cindefinite integral of the antiderivative ofநுண்கணிதம்தொகையீடு∫ab f(x) dx means the signed பரப்பளவு between the x-axis and the graph of the function f between x = a and x = b.∫0b x2  dx = b3/3;integral from … to … of … with respect toநுண்கணிதம்∮contour integral or closed line integralSimilar to the integral, but used to denote a single integration over a closed curve or loop.  It is sometimes used in physics texts involving equations regarding Gauss's Law, and while these formulas involve a closed surface integral, the representations describe only the first integration of the volume over the enclosing surface.  Instances where the latter requires simultaneous double integration, the symbol  would be more appropriate.  A third related symbol is the closed volume integral, denoted by the symbol .
The contour integral can also frequently be found with a subscript capital letter C, ∮C, denoting that a closed loop integral is, in fact, around a contour C, or sometimes dually appropriately, a circle C.  In representations of Gauss's Law, a subscript capital S, ∮S, is used to denote that the integration is over a closed surface.contour integral ofநுண்கணிதம்∇ gradient∇f (x1, …, xn) is the vector of partial derivatives (∂f / ∂x1, …, ∂f / ∂xn).If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z)டெல் இயக்கி, nabla, gradient ofvector calculus விரிதல் (திசையன் நுண்கணிதம்)If , then .del dot, divergence ofvector calculus curlIf , then .curl ofvector calculus∂partial differential With f (x1, …,  xn), ∂f/∂xi is the derivative of f with respect to xi, with all other variables kept constant. If f(x,y) := x2y, then ∂f/∂x = 2xypartial, dநுண்கணிதம்boundary ∂M means the boundary of M ∂{x : ||x|| ≤ 2} = {x : ||x|| = 2}boundary ofஇடவியல்⊥செங்குத்துx ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y.If l ⊥ m and m ⊥ n then l || n.is perpendicular toவடிவவியல்bottom elementx = ⊥ means x is the smallest element.∀x : x ∧ ⊥ = ⊥the bottom elementlattice theory||சமாந்தரம்x || y means x is parallel to y.If l || m and m ⊥ n then l ⊥ n.is parallel toவடிவவியல் entailment A  B means the sentence A entails the sentence B, that is in every model in which A is true, B is also true. A  A ∨ ¬Aentails model theory inferencex  y means y is derived from x. A → B  ¬B → ¬Ainfers or is derived frompropositional logic, predicate logic இயல்நிலை உட்குலம் N  G means that N is a normal subgroup of group G. Z(G)  Gis a normal subgroup ofகுலக் கோட்பாடு/ஈவு குலம் G / H means the quotient of group G modulo its subgroup H. {0, a, 2a, b, b+a, b+2a} / {0, b} = , {a, b+a},  mod குலக் கோட்பாடுquotient set A/~ means the set of all ~ சமானப் பகுதிes in A. If we define ~ by x ~ y ⇔ x − y ∈ , then /~ = {{x + n : n ∈ } : x ∈ (0,1]) mod கணக் கோட்பாடு≈approximately equalx ≈ y means x is approximately equal to y.π ≈ 3.14159is approximately equal toeverywhereisomorphism G ≈ H means that group G is isomorphic to group H. Q / {1, −1} ≈ V, where Q is the quaternion group and V is the கிளைன் நான்குறுப்புக்குலம். is isomorphic to குலக் கோட்பாடு~same order of magnitude m ~ n means the quantities m and n have the same order of magnitude, or general size. (Note that ~ is used for an approximation that is poor, otherwise use  ≈ .)2 ~ 5 8 × 9 ~ 100 but π2 ≈ 10roughly similar poorly approximatesஅண்ணளவாக்கக் கோட்பாடு〈,〉( | )< , >·:inner product〈x,y〉 means the inner product of x and y as defined in an inner product space. 
For spatial vectors, the புள்ளிப் பெருக்கல் notation, x·y is common. 
For matricies, the colon notation may be used.The standard inner product between two vectors x = (2, 3) and y = (−1, 5) is:〈x, y〉 = 2 × −1 + 3 × 5 = 13inner product ofநேரியல் இயற்கணிதம்tensor product V  U means the tensor product of V and U. {1, 2, 3, 4}  {1, 1, 2} =  , {1, 2, 3, 4},  tensor product of நேரியல் இயற்கணிதம்*convolution f * g means the convolution of f and g.  convolution, convoluted with functional analysisகூட்டுச்சராசரி (often read as "x bar") is the கூட்டுச்சராசரி (average value of )..overbar, … barபுள்ளியியல்<div style="font-size:200%;">complex conjugate is the complex conjugate of z.conjugateசிக்கலெண்delta equal to means equal by definition. When  is used, equality is not true generally, but rather equality is true under certain assumptions that are taken in context. Some writers prefer ≡..equal by definitioneverywhere

 See also 
 Mathematical alphanumeric symbols
 Table of logic symbols
 கணிதக் குறியீடுகள்
 ISO 31-11
 Roman letters used in mathematics
 Greek letters used in mathematics
 Notation in probability
 இயற்பியல் மாறிலிs
 Variables commonly used in physics

 External links 
 Jeff Miller: Earliest Uses of Various Mathematical Symbols
 TCAEP – Institute of Physics 
 GIF and PNG Images for Math Symbols
 Mathematical Symbols in Unicode 

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பகுப்பு:தரமுயர்த்தப்பட வேண்டிய கட்டுரைகள்