The equal sign x = y means that x and y are the same thing or their values are equal. 1+ 1 = 2 equals all fields.

The equal sign x ≠ y means that x and y are not the same thing or value. 1 ≠ 2 is not equal to all fields.

& gt

Strictly unequal x

X>y means that x is greater than y. 3 & lt； four

5>4 is less than and greater than ≤

≥

The equal sign x ≤ y means that x is less than or equal to y.

X ≥ y means that x is greater than or equal to y.3 ≤ 4; 5 ≤ 5

5 ≥ 4; 5 ≥ 5 less than or equal to, greater than or equal to order theory+

The plus sign 4+6 means 4 plus 6. 2+7 = 9 plus arithmetic? 6? 1

Negative 9? 6? 1 4 means 9 minus 4. 8 ? 6? 1 3 = 5 minus the arithmetic negative sign? 6? 13 stands for the negative number 3. ? 6? 1(? 6? 15) = 5 negative arithmetic complement set a? 6? 1 B represents a set containing all elements belonging to A but not to B. {1, 2,4}? 6? 1 {1, 3,4} = {2} negative set theory ×

The multiplication sign 3 × 4 means 3 times 4. 7 × 8 = 56 times the arithmetic direct product X × Y means that the first element belongs to X and the second element belongs to the set of ordered pairs of Y {1, 2 }× {3,4} = {(1, 3), (1, 4), (2,3). 6? 1 1) = (? 6? 122, 16, ? 6? 12) cross product vector algebra

/

The division symbol 6 ÷ 3 or 6/3 means that 6 is divided by 3. 2 ÷ 4 = 0.5

12/4 = 3 divided by arithmetic √

The root sign √x means a positive number whose square is x. The square root of √ 4 = 2 ... If the complex number z = r exp(iφ) is expressed in polar coordinates (satisfying-π < φ≤π), then √z = √r exp(iφ/2). √ (-1) = square root complex of I ... ||

The absolute value |x| represents the distance between x and 0 on the real number axis (or complex plane). |3| = 3, |-5| = |5|

|i| = 1, | 3+4i | = 5 ... Absolute number!

Factorial n! Represents the continuous product 1× 2× …× n. 4! Factor combination theory of = 1× 2× 3× 4 = 24 ...

Probability distribution X ~ D means that the probability distribution of random variable x is d. X ~ N(0, 1): Does the standard normal distribution satisfy the distribution statistics? 6? 0

→

6? four

Substantive meaning a? 6? 0 B means that a is true and b is true; A is false and B is uncertain.

→ May and? 6? 0, or has the meaning of the function mentioned below.

6? May 4 th and? 6? 0, or has the meaning of the parent set mentioned below. x = 2？ 6? 0 x2 = 4 is true, but x2 = 4? 6? 0 x = 2 is generally false (because x can be? 6? 12)。 Deduction, if … then … propositional logic? 6? 2

6? 2

Substantial equivalence a? 6? 2 B means that a is true, b is true, a is false and b is false. x + 5 = y +2？ 6? 2 x+3 = y if and only if propositional logic? 0? 1

0? 0

Logic is not a proposition? 0? 1A is true if and only if a is false.

Passing slashes through symbols is equivalent to putting "? 0? 1 "is placed before this symbol. ? 0? 1(? 0? 1A)？ 6? 2 A

x ≠ y？ 6? 2 ? 0? 1(x = y) not, not propositional logic

Logical AND or operation If A is true and B is true, then the proposition A ∧ B is true; Otherwise it's fake. n & lt4∧n & gt； 2 ? 6? 2 n = 3, when n is a natural number and propositional logic, lattice theory∨

Logical OR or AND operation If A or B (or both) is true, the proposition A ∨ B is true; If both are false, the proposition is false. n ≥ 4 ∨ n ≤ 2？ 6? 2 n ≠ 3, when n is a natural number or propositional logic, lattice theory

⊕

6? seven

XOR If only one of A and B is true, then the proposition A ⊕ B is true.

Answer? 6? 7 B means the same thing. (? 0? 1AA ⊕ A is always true and ⊕ A is always false. XOR propositional logic, Boolean algebra? 6? six

Full name quantifier? 6? 6 x: P(x) means that P(x) is true for all X. 6? 6 n ∈ N: n2 ≥ n is all; Do as you please; For any predicate logic? 6? nine

Existential quantifier? 6? 9 x: P(x) means that at least one x makes P(x) true. ? 6? 9 n ∈ N: n nIs there no predicate logic for even numbers? 6? 9!

Unique quantifier? 6? 9! X: P(x) means that only one x makes P(x) true. ? 6? 9! N ∈ N: n+5 = 2n There is unique predicate logic: =

≡

:? 6? 2

The definition of x := y or x ≡ y refers to a name, where X is defined as Y (Note: ≡ can also mean other meaning, just like Yu).

p:？ 6? 2 Q means that p is defined as the logical equivalent of q, cosh x := (1/2)(exp x+exp (? 6? 1x))

A XOR B:？ 6? 2 (A ∨ B) ∧？ 0? 1(A ∧ B) is defined as all fields {,}

The set brackets {a, b, c} represent the set theory of the set N = {0, 1, 2, ...} ...} {:}

{ | }

The set construction token {x: P(x)} represents the set of all x's satisfying P(x).

{x | P(x)} and {x: P(x)} have the same meaning. { n∈& lt； strong & gtN & lt/strong & gt； : n2 & lt20} = {0, 1, 2, 3, 4} satisfies the set theory of? 6? 1

{}

Empty set? 6? 1 represents a collection without elements.

{} also means this. { n∈& lt； strong & gtN & lt/strong & gt； : 1 & lt； n2 & lt4} = ? 6? Set theory of 1 empty set ∏

6? four

Set belonging to a ∈ S means that A belongs to set S; Answer? 6? 4 S means that a does not belong to S. (1/2)? 6? 1 1 ∈ N

2? 6? 1 1 ? 6? 4 N belongs to; Not all areas? 6? seven

6? three

Subset a? 6? 7 B means that all elements of a belong to B.

Answer? 6? 3 B stands for a 6? 7 B but a ≠ B. A ∩ B? 6? 7a； q？ 6? Subset set theory of 3 R… 6? eight

6? four

Parent set a? 6? 8 B means that all elements of b belong to a.

Answer? 6? 4 B stands for a 6? 8 B but A ≠ B A ∪ B? 6? 8b； r？ 6? Set theory of 4Q mother set ...

The union A ∪ B represents a set containing all elements of A and B but not any other elements. Answer? 6? 7 B？ 6? Union theory of 2 & ampnbspa∪b = b ... and ...

The intersection A ∩ B represents a set containing all elements belonging to a and B. strong & gtR & lt/strong & gt； : x2 = 1} ∩ n = {1} ... and intersection theory. ...

Complement set A \ B represents the set of all elements belonging to A but not to B, {1, 2,3,4} \ {3,4,5,6} = {1,2} minus; Delete set theory ()

The function uses f(x) to represent the value of f at x, and F(x) := x2, then f(3) = 32 = 9. F(x) set theory gives priority to combination, and the operation in brackets is carried out first. (8/4)/2 = 2/2 = 1; 8/(4/2) = 8/2 = 4 All fields? 0? 6 :X

→Y

Function arrow? 0? What does 6: X → Y mean? 0? Six mappings from set x to set y. Assemble? 0? 6: Z → N is defined as? 0? 6(x) = x2. From … to … Set Theory? 6? five

Compound function f? 6? 5g is a (f? 6? 5g)(x) = f(g(x)). If f(x) = 2x and g(x) = x+3, then (fog) (x) = 2(x+3). Compound set theory

ordinary

6? three

The natural number n stands for {0, 1, 2, 3, ...}. For another definition, please refer to the natural number entry. {|a|: a ∈ Z} = NN number

Z

6? six

The integer z stands for {…,? 6? 13,? 6? 12,? 6? 1 1,0, 1,2,3,…}。 { a:| a |∈& lt； strong & gtN & lt/strong & gt； } = ZZ number

Q

6? seven

The rational number q represents {p/q: p, q ∈.

π ? 6? 4 QQ number

rare

6? 0

The real number r stands for {limn→∞ an:? 6? 6n∈& lt； strong & gtN & lt/strong & gt； :an∈& lt； strong & gtQ & lt/strong & gt； Limit exists. π ∈ R

√(? 6? 1 1) ? 6? 4 RR number

C

6? seven

Complex number c means {a+bi: a, b ∈.

Infinite infinity is a number greater than any real number on the extended real number axis; Usually appears in the limit. Limx → 01| x | = ∞ infinite π

Pi stands for the ratio of circumference to diameter. A = πr？ 0? 5 is the geometric area π of a circle with radius r |||||.

Norm |||||||| X ||| is the norm of normed linear space element X ||||||||| ≤||||||||||||||||||||||| | | | ...; Length linear algebra ∑ ...

Sum ∑k= 1n ak means A 1+A2+…+an. ∑k = 14k 2 = 12+22+32+42 = 1+4+9+ 16 = 36。

The quadrature ∏k= 1n ak means a 1a2 an. ∏k = 14(k+2)=( 1+2)(2+2)(3+2)(4+2)。 Theory of direct product set of ∏n = 13r = rn ...

The reciprocal of the derivative f '(x) function f at point x, that is, the tangent slope there. If f(x) = x2, then f '(x) = 2x… prime number; Derivative calculus of ...

Indefinite integral or anti-derivative ∫ f(x) dx means indefinite integral of function with derivative f ∫ x2dx = x3/3 ...; The definite integral ∫ab f(x) dx of the inverse derivative calculus of ∫ represents the signed region ∫ 0bx2dx = b3/3 between x = a and x = b; From … to … Integral calculus with … as a variable? 6? three

Gradient? 6? A vector (df/dx 1, …, df/dxn) composed of the partial derivative of 3f (x 1, …, df/dxn). If f (x, y, z) = 3xy+z? 0? Five? 6? 3f = (3y, 3x, 2z) ... (del or nabla or gradient) calculus? 6? eight

The partial derivatives are f (x 1, …, xn),? 6? 8f/？ 6? When other variables remain the same, 8xi is the derivative of f to xi. If f(x, y) = x2y, then? 6? 8f/？ 6? The boundary of partial derivative calculus with 8x = 2xy ...? 6? 8M represents the boundary of m? 6? 8{x : ||x|| ≤ 2} =

Boundary topology ⊥ of {x: |||| x || = 2} ...

Vertical x ⊥ y means that x is vertical to y; More generally, X is orthogonal to Y. If l⊥m and m⊥n, then L || n. The element perpendicular to the geometric base x = ⊥ indicates that X is the smallest element. 6? 6x: x ∧ ⊥ = ⊥ elementary lattice theory? 6? seven

Include one? 6? 7 B means that A contains B, and in every model in which A holds, B also holds. 6? 7 A ∨？ 0? 1A meaning; Model theory? 6? three

Export x? 6? 3 y means that y is derived from x A → B? 6? 3 ? 0? 1B →? 0? 1A Derive propositional logic and predicate logic from? 7? seven

Regular subgroup n? 7? 7 G means that n is a regular subgroup of g. Z(G)? 7? 7 G is the regular subgroup group theory of …

The quotient group G/H represents the quotient group of subgroup H of G module. Module group theory {0, a, 2a, b, b+a, b+2a}/{0, b} = {{0, b}, {a, b+a}, {2a, b+2a}}.

Isomorphism G ≈ H means that g is isomorphic to HQ/{ 1,? 6? 1 1} ≈ V，

Where q is a quaternion group and v is a Klein group. Reference/thread-114418-1.html.