Tabel lambang matematis: Béda antarrépisi
Budhi (obrolan | kontribusi) Tidak ada ringkasan suntingan |
Budhi (obrolan | kontribusi) |
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Baris ka-367: | Baris ka-367: | ||
The article [[wikipedia: How does one edit a page]] contains information about how to produce these math symbols in Wikipedia articles. |
The article [[wikipedia: How does one edit a page]] contains information about how to produce these math symbols in Wikipedia articles. |
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==Tumbu kaluar== |
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* Jeff Miller: ''Earliest Uses of Various Mathematical Symbols, http://members.aol.com/jeff570/mathsym.html |
* Jeff Miller: ''Earliest Uses of Various Mathematical Symbols, http://members.aol.com/jeff570/mathsym.html |
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* TCAEP - Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm |
* TCAEP - Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm |
Révisi nurutkeun 1 Séptémber 2004 06.49
Dina matematik, a set of symbols is frequently used in mathematical expressions. As mathematicians are familiar with these symbols, they are not explained each time they are used. So, for mathematical novices, the following table lists many common symbols together with their name, pronunciation and related field of mathematics. Additionally, the second line contains an informal definition, and the third line gives a short example.
Note: If some of the symbols don't display properly for you, then your browser does not completely implement the HTML 4 character entities, or you have to install additional fonts. You can check your browser here.
Symbol | Name | reads as | Category |
---|---|---|---|
+ | addition | plus | arithmetic |
4 + 6 = 10 means that if four is added to 6, the sum, or result, is 10. | |||
43 + 65 = 108; 2 + 7 = 9 | |||
− | subtraction | minus | arithmetic |
9 − 4 = 5 means that if 4 is subtracted from 9, the result will be 5. The minus sign also denotes that a number is negative. For example, 5 + (−3) = 2 means that if five and negative three are added, the result is two. | |||
87 − 36 = 51 | |||
⇒
| material implication | implies; if .. then | propositional logic |
A ⇒ 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 mentioned further down | |||
x = 2 ⇒ x2 = 4 is true, but x2 = 4 ⇒ x = 2 is in general false (since x could be −2) | |||
⇔
| material equivalence | if and only if; iff | propositional logic |
A ⇔ B means: A is true if B is true and A is false if B is false | |||
x + 5 = y + 2 ⇔ x + 3 = y | |||
∧ | 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 | |||
∨ | 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 | |||
¬
| 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) | |||
∀ | universal quantification | for all; for any; for each | predicate logic |
∀ x: P(x) means: P(x) is true for all x | |||
∀ n ∈ N: n2 ≥ n | |||
∃ | existential quantification | there exists | predicate logic |
∃ x: P(x) means: there is at least one x such that P(x) is true | |||
∃ n ∈ N: n + 5 = 2n | |||
= | equality | equals | everywhere |
x = y means: x and y are different names for precisely the same thing | |||
1 + 2 = 6 − 3 | |||
:=
| definition | is defined as | everywhere |
x := y or x ≡ y means: x is defined to be another name for y (but note that ≡ can also mean other things, such as 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) | |||
{ , } | set brackets | the set of ... | set theory |
{a,b,c} means: the set consisting of a, b, and c | |||
N = {0,1,2,...} | |||
{ : }
| set builder notation | the set of ... such that ... | set theory |
{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 ∈ N : n2 < 20} = {0,1,2,3,4} | |||
∅
| empty set | empty set | set theory |
{} means: the set with no elements; ∅ is the same thing | |||
{n ∈ N : 1 < n2 < 4} = {} | |||
∈
| set membership | in; is in; is an element of; is a member of; belongs to | set theory |
a ∈ S means: a is an element of the set S; a ∉ S means: a is not an element of S | |||
(1/2)−1 ∈ N; 2−1 ∉ N | |||
⊆
| subset | is a subset of | set theory |
A ⊆ B means: every element of A is also element of B A ⊂ B means: A ⊆ B but A ≠ B | |||
A ∩ B ⊆ A; Q ⊂ R | |||
∪ | set theoretic union | the union of ... and ...; union | set theory |
A ∪ B means: the set that contains all the elements from A and also all those from B, but no others | |||
A ⊆ B ⇔ A ∪ B = B | |||
∩ | set theoretic intersection | intersected with; intersect | set theory |
A ∩ B means: the set that contains all those elements that A and B have in common | |||
{x ∈ R : x2 = 1} ∩ N = {1} | |||
\ | set theoretic complement | minus; without | set theory |
A \ B means: the set that contains all those elements of A that are not in B | |||
{1,2,3,4} \ {3,4,5,6} = {1,2} | |||
( )
| function application; grouping | of | set theory |
for function application: f(x) means: 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 | |||
f:X→Y | function arrow | from ... to | functions |
f: X → Y means: the function f maps the set X into the set Y | |||
Consider the function f: Z → N defined by f(x) = x2 | |||
N | natural numbers | N | numbers |
N means {0,1,2,3,...}, but see the article on natural numbers for a different convention. | |||
{|a| : a ∈ Z} = N | |||
Z | integers | Z | numbers |
Z means: {...,−3,−2,−1,0,1,2,3,...} | |||
{a : |a| ∈ N} = Z | |||
Q | rational numbers | Q | numbers |
Q means: {p/q : p,q ∈ Z, q ≠ 0} | |||
3.14 ∈ Q; π ∉ Q | |||
R | real numbers | R | numbers |
R means: {limn→∞ an : ∀ n ∈ N: an ∈ Q, the limit exists} | |||
π ∈ R; √(−1) ∉ R | |||
C | complex numbers | C | numbers |
C means: {a + bi : a,b ∈ R} | |||
i = √(−1) ∈ C | |||
<
| comparison | is less than, is greater than | partial orders |
x < y means: x is less than y; x > y means: x is greater than y | |||
x < y ⇔ y > x | |||
≤
| comparison | is less than or equal to, is greater than or equal to | partial orders |
x ≤ y means: x is less than or equal to y; x ≥ y means: x is greater than or equal to y | |||
x ≥ 1 ⇒ x2 ≥ x | |||
√ | square root | the principal square root of; square root | real numbers |
√x means: the positive number whose square is x | |||
√(x2) = |x| | |||
∞ | infinity | infinity | numbers |
∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits | |||
limx→0 1/|x| = ∞ | |||
π | pi | pi | Euclidean geometry |
π means: the ratio of a circle's circumference to its diameter | |||
A = πr² is the area of a circle with radius r | |||
! | factorial | factorial | combinatorics |
n! is the product 1×2×...×n | |||
4! = 24 | |||
| | | absolute value | absolute value of | numbers |
|x| means: the distance in the real line (or the complex plane) between x and zero | |||
|a + bi| = √(a2 + b2) | |||
|| || | norm | norm of; length of | functional analysis |
||x|| is the norm of the element x of a normed vector space | |||
||x+y|| ≤ ||x|| + ||y|| | |||
∑ | summation | sum over ... from ... to ... of | arithmetic |
∑k=1n ak means: a1 + a2 + ... + an | |||
∑k=14 k2 = 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30 | |||
∏ | product | product over ... from ... to ... of | arithmetic |
∏k=1n ak means: a1a2···an | |||
∏k=14 (k + 2) = (1 + 2)(2 + 2)(3 + 2)(4 + 2) = 3 × 4 × 5 × 6 = 360 | |||
∫ | integration | integral from ... to ... of ... with respect to | calculus |
∫ab f(x) dx means: 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 | |||
f ' | 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 | |||
∇ | 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.gif (Gambar:Del.gif). | |||
∂ | 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 | |||
⊥ | perpendicular | is perpendicular to | orthogonality |
x ⊥ y means: x is perpendicular to y; or more generally x is orthogonal to y. | |||
⊥ | bottom element | the bottom element | lattice theory |
x = ⊥ means: x is the smallest element. | |||
insert more (suggestions are the inequality symbols); some symbols are used in examples before they are defined | |||
If some of these symbols are used in a Wikipedia article that is intended for beginners, it may be a good idea to include a statement like the following, (below the definition of the subject), in order to reach a broader audience:
- ''This article uses [[table of mathematical symbols|mathematical symbols]].''
The article wikipedia: How does one edit a page contains information about how to produce these math symbols in Wikipedia articles.
Tumbu kaluar
- Jeff Miller: Earliest Uses of Various Mathematical Symbols, http://members.aol.com/jeff570/mathsym.html
- TCAEP - Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm