গাণিতিক চিহ্নের সারণি

উইকিপিডিয়া, মুক্ত বিশ্বকোষ থেকে

সূচিপত্র

১ মূল চিহ্নসমূহের তালিকা
২ আরও দেখুন
৩ বহিঃসংযোগ
৪ বিশেষ চিহ্নসমূহ

[সম্পাদনা করুন] মূল চিহ্নসমূহের তালিকা

চিহ্ন	নাম	ব্যাখ্যা	উদাহরণ
	যেভাবে পড়তে হবে
	বিষয়শ্রেণী
=	সমতা	x = y অর্থ x ও y একই জিনিস অথবা মান	১ + ২ = ৩
	সমান সমান; সমান
	সবক্ষেত্রে
≠ <> !=	অসমান	x ≠ y অর্থ x এবং y একই জিনিস নয় অথবা তাদের মান সমান নয়	1 ≠ 2
	অসমান
	সবক্ষেত্রে
< > ≪ ≫	অসমতা	x < y অর্থ x y থেকে ক্ষুদ্রতর x > y অর্থ x y থেকে বৃহত্তর x ≪ y অর্থ x y থেকে অনেক ক্ষুদ্রতর x ≫ y অর্থ x y থেকে অনেক বৃহত্তর	৩ < ৪ ৫ > ৩ ০.০০৭ ≪ ১০০০০০০০
	ক্ষুদ্রতর, বৃহত্তর, অনেক ছোট, অনেক বড়
	order theory
≤ ≥	অসমতা	x ≤ y অর্থ x y এর চেয়ে ছোট বা সমান x ≥ y অর্থ x y এর চেয়ে বড় বা সমান	৩ ≤ ৪ এবং ৫ ≤ ৫ ৫ ≥ ৪ এবং ৫ ≥ ৫
	ক্ষুদ্রতর অথবা সমান, বৃহত্তর অথবা সমান
	order theory
∝	সমানুপাত	y ∝ x অর্থ y = kx , কোন ধ্রুবক k এর জন্য	যদি y = 2x, তাহলে y ∝ x
	সমানুপাতিক
	সবক্ষেত্রে
+	যোগ	৪ + ৬ অর্থ ৪ ও ৬ এর যোগফল	২ + ৭ = ৯
	যোগ
	গণিত
	disjoint union	A₁ + A₂ অর্থ the disjoint union of sets A₁ and A₂.	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)}
	the disjoint union of ... and ...
	set theory
−	subtraction	9 − 4 অর্থ the subtraction of 4 from 9.	8 − 3 = 5
	minus
	arithmetic
	negative sign	−3 অর্থ the negative of the number 3.	−(−5) = 5
	negative ; minus
	arithmetic
	set-theoretic complement	A − B অর্থ the set that contains all the elements of A that are not in B.	{1,2,4} − {1,3,4} = {2}
	minus; without
	set theory
×	multiplication	3 × 4 অর্থ the multiplication of 3 by 4.	7 × 8 = 56
	times
	arithmetic
	Cartesian product	X×Y অর্থ the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y.	{1,2} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}
	the Cartesian product of ... and ...; the direct product of ... and ...
	set theory
	cross product	u × v অর্থ the cross product of vectors u and v	(1,2,5) × (3,4,−1) = (−22, 16, − 2)
	cross
	vector algebra
÷ /	division	6 ÷ 3 or 6/3 অর্থ the division of 6 by 3.	2 ÷ 4 = .5 12/4 = 3
	divided by
	arithmetic
√	square root	√x অর্থ the positive number whose square is x.	√4 = 2
	the principal square root of; square root
	real numbers
	complex square root	if z = r exp(iφ) is represented in polar coordinates with -π < φ ≤ π, then √z = √r exp(iφ/2).	√(-1) = i
	the complex square root of; square root
	complex numbers
\| \|	absolute value	\|x\| অর্থ the distance in the real line (or the complex plane) between x and zero.	\|3\| = 3, \|-5\| = \|5\| \|i\| = 1, \|3+4i\| = 5
	absolute value of
	numbers
!	factorial	n! is the product 1 × 2× ... × n.	4! = 1 × 2 × 3 × 4 = 24
	factorial
	combinatorics
~	probability distribution	X ~ D, অর্থ the random variable X has the probability distribution D.	X ~ N(0,1), the standard normal distribution
	has distribution
	statistics
⇒ → ⊃	material implication	A ⇒ B অর্থ 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 .. then
	propositional logic
⇔ ↔	material equivalence	A ⇔ B অর্থ A is true if B is true and A is false if B is false.	x + 5 = y +2 ⇔ x + 3 = y
	if and only if; iff
	propositional logic
¬ ˜	logical negation	The statement ¬A is true if and only if A is false. A slash placed through another operator is the same as "¬" placed in front.	¬(¬A) ⇔ A x ≠ y ⇔ ¬(x = y)
	not
	propositional logic
∧	logical conjunction or meet in a lattice	The statement A ∧ B is true if A and B are both true; else it is false.	n < 4 ∧ n >2 ⇔ n = 3 when n is a natural number.
	and
	propositional logic, lattice theory
∨	logical disjunction or join in a lattice	The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false.	n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.
	or
	propositional logic, lattice theory
⊕ ⊻	exclusive or	The statement A ⊕ B is true when either A or B, but not both, are true. A ⊻ B অর্থ the same.	(¬A) ⊕ A is always true, A ⊕ A is always false.
	xor
	propositional logic, Boolean algebra
∀	universal quantification	∀ x: P(x) অর্থ P(x) is true for all x.	∀ n ∈ N: n² ≥ n.
	for all; for any; for each
	predicate logic
∃	existential quantification	∃ x: P(x) অর্থ there is at least one x such that P(x) is true.	∃ n ∈ N: n is even.
	there exists
	predicate logic
∃!	uniqueness quantification	∃! x: P(x) অর্থ there is exactly one x such that P(x) is true.	∃! n ∈ N: n + 5 = 2n.
	there exists exactly one
	predicate logic
:= ≡ :⇔	definition	x := y or x ≡ y অর্থ x is defined to be another name for y (but note that ≡ can also mean other things, such as congruence). P :⇔ Q অর্থ 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 as
	সবক্ষেত্রে
{ , }	set brackets	{a,b,c} অর্থ the set consisting of a, b, and c.	N = {0, 1, 2, ...}
	the set of ...
	set theory
{ : } { \| }	set builder notation	{x : P(x)} অর্থ the set of all x for which P(x) is true. {x \| P(x)} is the same as {x : P(x)}.	{n ∈ N : n² < 20} = {0, 1, 2, 3, 4}
	the set of ... such that ...
	set theory
∅ {}	empty set	∅ অর্থ the set with no elements. {} অর্থ the same.	{n ∈ N : 1 < n² < 4} = ∅
	the empty set
	set theory
∈ ∉	set membership	a ∈ S অর্থ a is an element of the set S; a ∉ S অর্থ a is not an element of S.	(1/2)⁻¹ ∈ N 2⁻¹ ∉ N
	is an element of; is not an element of
	সবক্ষেত্রে, set theory
⊆ ⊂	subset	(subset) A ⊆ B অর্থ every element of A is also element of B. (proper subset) A ⊂ B অর্থ A ⊆ B but A ≠ B.	A ∩ B ⊆ A; Q ⊂ R
	is a subset of
	set theory
⊇ ⊃	superset	A ⊇ B অর্থ every element of B is also element of A. A ⊃ B অর্থ A ⊇ B but A ≠ B.	A ∪ B ⊇ B; R ⊃ Q
	is a superset of
	set theory
∪	set-theoretic union	(exclusive) A ∪ B অর্থ 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 অর্থ 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 ...; union
	set theory
∩	set-theoretic intersection	A ∩ B অর্থ the set that contains all those elements that A and B have in common.	{x ∈ R : x² = 1} ∩ N = {1}
	intersected with; intersect
	set theory
\	set-theoretic complement	A \ B অর্থ the set that contains all those elements of A that are not in B.	{1,2,3,4} \ {3,4,5,6} = {1,2}
	minus; without
	set theory
( )	function application	f(x) অর্থ the value of the function f at the element x.	If f(x) := x², then f(3) = 3² = 9.
	of
	set theory
	precedence grouping	Perform the operations inside the parentheses first.	(8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.
	parentheses
	সবক্ষেত্রে
f:X→Y	function arrow	f: X → Y অর্থ the function f maps the set X into the set Y.	Let f: Z → N be defined by f(x) := x².
	from ... to
	set theory
o	function composition	fog 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 with
	set theory
N ℕ	natural numbers	N অর্থ {0, 1, 2, 3, ...}, but see the article on natural numbers for a different convention.	{\|a\| : a ∈ Z} = N
	N
	numbers
Z ℤ	integers	Z অর্থ {..., −3, −2, −1, 0, 1, 2, 3, ...}.	{a, -a : a ∈ N} = Z
	Z
	numbers
Q ℚ	rational numbers	Q অর্থ {p/q : p,q ∈ Z, q ≠ 0}.	3.14 ∈ Q π ∉ Q
	Q
	numbers
R ℝ	real numbers	R অর্থ the set of real numbers.	π ∈ R √(−1) ∉ R
	R
	numbers
C ℂ	complex numbers	C অর্থ {a + bi : a,b ∈ R}.	i = √(−1) ∈ C
	C
	numbers
	arbitrary 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
	C
	integral calculus
∞	infinity	∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits.	lim_x→0 1/\|x\| = ∞
	infinity
	numbers
$π$	pi	π is the ratio of a circle's circumference to its diameter. Its value is 3.1415....	A = πr² is the area of a circle with radius r
	pi
	Euclidean geometry
\|\| \|\|	norm	\|\|x\|\| is the norm of the element x of a normed vector space.	\|\|x+y\|\| ≤ \|\|x\|\| + \|\|y\|\|
	norm of; length of
	linear algebra
∑	summation	$\sum_{k=1}^{n}{a_k}$ অর্থ a₁ + a₂ + ... + a_n.	$\sum_{k=1}^{4}{k^2}$ = 1² + 2² + 3² + 4² = 1 + 4 + 9 + 16 = 30
	sum over ... from ... to ... of
	arithmetic
∏	product	$\prod_{k=1}^na_k$ অর্থ a₁a₂•••a_n.	$\prod_{k=1}^4(k+2)$ = (1+2)(2+2)(3+2)(4+2) = 3 × 4 × 5 × 6 = 360
	product over ... from ... to ... of
	arithmetic
	Cartesian product	$\prod_{i=0}^{n}{Y_i}$ অর্থ the set of all (n+1)-tuples (y₀,...,y_n).	$\prod_{n=1}^{3}{\mathbb{R}} = \mathbb{R}\times\mathbb{R}\times\mathbb{R} = \mathbb{R}^3$
	the Cartesian product of; the direct product of
	set theory
'	derivative	f '(x) is the derivative of the function f at the point x, i.e., the slope of the tangent to f at x.	If f(x) := x², then f '(x) = 2x
	... prime; derivative of ...
	calculus
∫	indefinite integral or antiderivative	∫ f(x) dx অর্থ a function whose derivative is f.	∫x² dx = x³/3 + C
	indefinite integral of ...;; the antiderivative of ...
	calculus
	definite integral	∫_a^b f(x) dx অর্থ the signed area between the x-axis and the graph of the function f between x = a and x = b.	∫₀^b x² dx = b³/3;
	integral from ... to ... of ... with respect to
	calculus
∇	gradient	∇f (x₁, …, x_n) is the vector of partial derivatives (df / dx₁, …, df / dx_n).	If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z)
	del, nabla, gradient of
	calculus
∂	partial derivative	With f (x₁, …, x_n), ∂f/∂x_i is the derivative of f with respect to x_i, with all other variables kept constant.	If f(x,y) := x²y, then ∂f/∂x = 2xy
	partial derivative of
	calculus
	boundary	∂M অর্থ the boundary of M	∂{x : \|\|x\|\| ≤ 2} = {x : \|\|x\|\| = 2}
	boundary of
	topology
⊥	perpendicular	x ⊥ y অর্থ x is perpendicular to y; or more generally x is orthogonal to y.	If l⊥m and m⊥n then l \|\| n.
	is perpendicular to
	geometry
	bottom element	x = ⊥ অর্থ x is the smallest element.	∀x : x ∧ ⊥ = ⊥
	the bottom element
	lattice theory
⊧	entailment	A ⊧ B অর্থ the sentence A entails the sentence B, that is every model in which A is true, B is also true.	A ⊧ A ∨ ¬A
	entails
	model theory
⊢	inference	x ⊢ y অর্থ y is derived from x.	A → B ⊢ ¬B → ¬A
	infers or is derived from
	propositional logic, predicate logic
◅	normal subgroup	N ◅ G অর্থ that N is a normal subgroup of group G.	Z(G) ◅ G
	is a normal subgroup of
	group theory
/	quotient group	G/H অর্থ the quotient of group G modulo its subgroup H.	{0, a, 2a, b, b+a, b+2a} / {0, b} = {{0, b}, {a, b+a}, {2a, b+2a}}
	mod
	group theory
	quotient set	A/~ অর্থ the set of all ~ equivalence classes in A.

	set theory
≈	isomorphism	G ≈ H অর্থ that group G is isomorphic to group H	Q / {1, −1} ≈ V, where Q is the quaternion group and V is the Klein four-group.
	is isomorphic to
	group theory
	approximately equal	x ≈ y অর্থ x is approximately equal to y	π ≈ 3.14159
	is approximately equal to
	সবক্ষেত্রে
⊗	tensor product	V ⊗ U অর্থ the tensor product of V and U.	{1, 2, 3, 4} ⊗ {1,1,2} = {{1, 2, 3, 4}, {1, 2, 3, 4}, {2, 4, 6, 8}}
	tensor product of
	linear algebra

[সম্পাদনা করুন] আরও দেখুন

Mathematical alphanumeric symbols
গাঠনিক ধ্রুবক
পদার্থবিজ্ঞানের চলক
আই এস ও ৩১-১১

[সম্পাদনা করুন] বিশেষ চিহ্নসমূহ

Technical note: Due to technical limitations, many computers cannot display some of the special characters in this article. Such characters may be rendered as boxes, question marks, or other nonsense symbols, depending on your browser, operating system, and installed fonts. Even if you have ensured that your browser is interpreting the article as UTF-8 encoded and you have installed a font that supports a wide range of Unicode, such as Code2000, Arial Unicode MS, Lucida Sans Unicode or one of the free Unicode fonts, you may still need to use a different browser, as browser capabilities in this regard tend to vary.