Tabel Lambang Matematis
Matematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna.
Pikeun nu icikibung dina widang matematik mah, moal kukumaha, tapi pikeun nu arang nempo, sigana kudu mindeng ngapalkeun. Di handap ieu dibéréndélkeun rupa-rupa lambang matematis katut ngarana, éjahanana, jeung saeutik dadaranana.
Catetan: Mun sababaraha lambang teu némbongan sakumaha mistina, panyaksrak anjeun can sagemblengna ngalarapkeun HTML 4 character entities, atawa anjeun kudu nginstal aksara tambahan. Anjeun bisa mariksa panyaksrak anjeun di dieu.
| Lambang | Ngaran | Dibaca | Kategori |
|---|---|---|---|
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | tambah | plus | aritmétik |
| 4 + 6 = 10 nu hartina mun opat ditambahkeun ka genep, jumlahna, atawa hasilna, nyéta 10. | |||
| 43 + 65 = 108; 2 + 7 = 9 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | kurang | minus | aritmétik |
| 9 − 4 = 5 nu hartina mun salapan dikurangan opat, hasilna bakal lima. Tanda minus ogé nandakeun yén hiji angka négatif. Pikeun conto, 5 + (−3) = 2 hartina mun lima ditambahkeun jeung négatif tilu, hasilna dua. | |||
| 36 − 5 = 31 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | material implication | implies; if .. then | propositional logic |
| A ⇒ B méans: if A is true then B is also true; if A is false then nothing is said about B. → may méan the same as ⇒, or it may have the méaning for functions mentioned further down | |||
| x = 2 ⇒ x2 = 4 is true, but x2 = 4 ⇒ x = 2 is in general false (since x could be −2) | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | material equivalence | if and only if; iff | propositional logic |
| A ⇔ B méans: A is true if B is true and A is false if B is false | |||
| x + 5 = y + 2 ⇔ x + 3 = y | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | logical conjunction or meet in a lattice | and | propositional logic, lattice theory |
| 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 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | logical disjunction or join in a lattice | or | propositional logic, lattice theory |
| 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 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | logical negation | not | propositional logic |
| 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 ∧ B) ⇔ (¬A) ∨ (¬B); x ∉ S ⇔ ¬(x ∈ S) | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | universal quantification | for all; for any; for éach | predicate logic |
| ∀ x: P(x) méans: P(x) is true for all x | |||
| ∀ n ∈ N: n2 ≥ n | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | existential quantification | there exists | predicate logic |
| ∃ x: P(x) méans: there is at léast one x such that P(x) is true | |||
| ∃ n ∈ N: n + 5 = 2n | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | equality | equals | everywhere |
| x = y méans: x and y are different names for precisely the same thing | |||
| 1 + 2 = 6 − 3 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | definition | is defined as | everywhere |
| x := y or x ≡ y méans: x is defined to be another name for y (but note that ≡ can also méan other things, such as congruence) P :⇔ Q méans: P is defined to be logically equivalent to Q | |||
| cosh x := (1/2)(exp x + exp (−x)); A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B) | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | set brackets | the set of ... | set theory |
| {a,b,c} méans: the set consisting of a, b, and c | |||
| N = {0,1,2,...} | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | set builder notation | the set of ... such that ... | set theory |
| {x : P(x)} méans: 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} | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | empty set | empty set | set theory |
| {} méans: the set with no elements; ∅ is the same thing | |||
| {n ∈ N : 1 < n2 < 4} = {} | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | set membership | in; is in; is an element of; is a member of; belongs to | set theory |
| a ∈ S méans: a is an element of the set S; a ∉ S méans: a is not an element of S | |||
| (1/2)−1 ∈ N; 2−1 ∉ N | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | subset | is a subset of | set theory |
| A ⊆ B méans: every element of A is also element of B A ⊂ B méans: A ⊆ B but A ≠ B | |||
| A ∩ B ⊆ A; Q ⊂ R | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | set theoretic union | the union of ... and ...; union | set theory |
| A ∪ B méans: the set that contains all the elements from A and also all those from B, but no others | |||
| A ⊆ B ⇔ A ∪ B = B | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | set theoretic intersection | intersected with; intersect | set theory |
| A ∩ B méans: the set that contains all those elements that A and B have in common | |||
| {x ∈ R : x2 = 1} ∩ N = {1} | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | set theoretic complement | minus; without | set theory |
| A \ B méans: the set that contains all those elements of A that are not in B | |||
| {1,2,3,4} \ {3,4,5,6} = {1,2} | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | function application; grouping | of | set theory |
| for function application: f(x) méans: the value of the function f at the element x for grouping: perform the operations inside the parentheses first | |||
| If f(x) := x2, then f(3) = 32 = 9; (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | function arrow | from ... to | functions |
| f: X → Y méans: the function f maps the set X into the set Y | |||
| Consider the function f: Z → N defined by f(x) = x2 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | natural numbers | N | numbers |
| N méans {0,1,2,3,...}, but see the article on natural numbers for a different convention. | |||
| {|a| : a ∈ Z} = N | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | integers | Z | numbers |
| Z méans: {...,−3,−2,−1,0,1,2,3,...} | |||
| {a : |a| ∈ N} = Z | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | rational numbers | Q | numbers |
| Q méans: {p/q : p,q ∈ Z, q ≠ 0} | |||
| 3.14 ∈ Q; π ∉ Q | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | real numbers | R | numbers |
| R méans: {limn→∞ an : ∀ n ∈ N: an ∈ Q, the limit exists} | |||
| π ∈ R; √(−1) ∉ R | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | complex numbers | C | numbers |
| C méans: {a + bi : a,b ∈ R} | |||
| i = √(−1) ∈ C | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | comparison | is less than, is gréater than | partial orders |
| x < y méans: x is less than y; x > y méans: x is gréater than y | |||
| x < y ⇔ y > x | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | comparison | is less than or equal to, is gréater than or equal to | partial orders |
| x ≤ y méans: x is less than or equal to y; x ≥ y méans: x is gréater than or equal to y | |||
| x ≥ 1 ⇒ x2 ≥ x | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | square root | the principal square root of; square root | real numbers |
| √x méans: the positive number whose square is x | |||
| √(x2) = |x| | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | infinity | infinity | numbers |
| ∞ is an element of the extended number line that is gréater than all réal numbers; it often occurs in limits | |||
| limx→0 1/|x| = ∞ | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | pi | pi | Euclidean geometry |
| π méans: the ratio of a circle's circumference to its diaméter | |||
| A = πr² is the aréa of a circle with radius r | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | factorial | factorial | combinatorics |
| n! is the product 1×2×...×n | |||
| 4! = 24 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | absolute value | absolute value of | numbers |
| |x| méans: the distance in the real line (or the complex plane) between x and zero | |||
| |a + bi| = √(a2 + b2) | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | norm | norm of; length of | functional analysis |
| ||x|| is the norm of the element x of a normed vector space | |||
| ||x+y|| ≤ ||x|| + ||y|| | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | summation | sum over ... from ... to ... of | arithmetic |
| ∑k=1n ak méans: a1 + a2 + ... + an | |||
| ∑k=14 k2 = 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | product | product over ... from ... to ... of | arithmetic |
| ∏k=1n ak méans: a1a2···an | |||
| ∏k=14 (k + 2) = (1 + 2)(2 + 2)(3 + 2)(4 + 2) = 3 × 4 × 5 × 6 = 360 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | integration | integral from ... to ... of ... with respect to | calculus |
| ∫ab f(x) dx méans: the signed area between the x-axis and the graph of the function f between x = a and x = b | |||
| ∫0b x2 dx = b3/3; ∫x2 dx = x3/3 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | derivative | derivative of f; f prime | calculus |
| f '(x) is the derivative of the function f at the point x, i.e., the slope of the tangent there | |||
| If f(x) = x2, then f '(x) = 2x and f ''(x) = 2 | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | gradient | del, nabla, gradient of | calculus |
| ∇f (x1, …, xn) is the vector of partial derivatives (df / dx1, …, df / dxn) | |||
| If f (x,y,z) = 3xy + z² then ∇f = (3y, 3x, 2z) A transparent image for text is: Image:Del.svg ( | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | partial | partial derivative of | calculus |
| 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 = 2xy | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | perpendicular | is perpendicular to | orthogonality |
| x ⊥ y méans: x is perpendicular to y; or more generally x is orthogonal to y. | |||
Tabel Lambang MatematisMatematika mindeng pisan ngagunakeunsakumpulan lambang pikeun éksprési matematisna. | bottom element | the bottom element | lattice theory |
| x = ⊥ méans: x is the smallest element. | |||
| insert more (suggestions are the inequality symbols); some symbols are used in examples before they are defined | |||
Mun sababaraha lambang ieu dipaké dina artikel Wikipédia, aya hadéna méré saeutik dadaran ngeunaan lambang éta.
Artikel Wikipédia:Cara ngédit kaca ngandung émbaran ngeunaan cara ngetikkeun lambangg-lambang matematis ieu na artikel Wikipédia.
Tumbu kaluar
- Jeff Miller: éarliest Uses of Various Mathematical Symbols, https://web.archive.org/web/20081204035420/http://members.aol.com/jeff570/mathsym.html
- TCAEP - Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm Archived 2004-08-29 di Wayback Machine
This article uses material from the Wikipedia Basa Sunda article Tabel lambang matematis, which is released under the Creative Commons Attribution-ShareAlike 3.0 license ("CC BY-SA 3.0"); additional terms may apply (view authors). Eusi nu nyangkaruk ditangtayungan ku CC BY-SA 4.0 iwal lamun disebutkeun béda. Images, videos and audio are available under their respective licenses.
®Wikipedia is a registered trademark of the Wiki Foundation, Inc. Wiki Basa Sunda (DUHOCTRUNGQUOC.VN) is an independent company and has no affiliation with Wiki Foundation.