基础运算
Plus
- 读法
- plus
- LaTeX
含义
Adds two quantities.
学习资料
数学符号说明
整理常用数学符号的读法、含义、LaTeX 命令、示例与 AI 提问思路的实用参考。
基础运算
Minus
- 读法
- minus
- LaTeX
含义
Subtracts one quantity from another, or marks a negative value.
示例
基础运算
Multiplication sign
- 读法
- times
- LaTeX
含义
Multiplies two quantities. In algebra, multiplication is often written with a dot or omitted.
示例
基础运算
Division sign
- 读法
- divided by
- LaTeX
含义
Divides one quantity by another nonzero quantity.
示例
基础运算
Fraction
- 读法
- a over b
- LaTeX
含义
Represents division or a ratio with a numerator and denominator.
示例
基础运算
Plus-minus
- 读法
- plus or minus
- LaTeX
含义
Indicates that both the positive and negative alternatives are being considered.
示例
基础运算
Square root
- 读法
- square root of x
- LaTeX
含义
The nonnegative value whose square is x, unless a different convention is stated.
示例
关系
Equals
- 读法
- equals
- LaTeX
含义
States that two expressions have the same value or represent the same object.
示例
关系
Not equal
- 读法
- is not equal to
- LaTeX
含义
Shows that two expressions do not have the same value.
示例
关系
Approximately equal
- 读法
- approximately equal to
- LaTeX
含义
Indicates a rounded or approximate value rather than exact equality.
示例
关系
Less than or equal to
- 读法
- less than or equal to
- LaTeX
含义
Allows equality while comparing two quantities.
示例
关系
Greater than or equal to
- 读法
- greater than or equal to
- LaTeX
含义
Compares two quantities while allowing equality.
示例
关系
Proportional to
- 读法
- is proportional to
- LaTeX
含义
Shows that one quantity changes by a constant multiple of another.
示例
集合论
Empty set
- 读法
- empty set
- LaTeX
含义
The set with no elements.
示例
集合论
Element of
- 读法
- is an element of
- LaTeX
含义
Shows that a value belongs to a set.
示例
集合论
Not an element of
- 读法
- is not an element of
- LaTeX
含义
Shows that a value does not belong to a set.
示例
集合论
Proper subset
- 读法
- is a proper subset of
- LaTeX
含义
Usually indicates that every element of one set is in another, and the two sets are not equal.
示例
集合论
Subset or equal
- 读法
- is a subset of or equal to
- LaTeX
含义
Allows two sets to be equal while stating subset inclusion.
示例
集合论
Union
- 读法
- union
- LaTeX
含义
Combines all elements that are in either set.
示例
集合论
Intersection
- 读法
- intersection
- LaTeX
含义
Keeps only the elements shared by both sets.
示例
逻辑
Universal quantifier
- 读法
- for all
- LaTeX
含义
States that a claim applies to every object in a domain.
示例
逻辑
Existential quantifier
- 读法
- there exists
- LaTeX
含义
States that at least one object satisfying a condition exists.
示例
逻辑
Negation
- 读法
- not
- LaTeX
含义
Reverses the truth value of a statement.
示例
逻辑
Logical and
- 读法
- and
- LaTeX
含义
True only when both connected statements are true.
示例
逻辑
Logical or
- 读法
- or
- LaTeX
含义
True when at least one connected statement is true.
示例
逻辑
Implication
- 读法
- implies
- LaTeX
含义
Connects a condition to a conclusion.
示例
逻辑
If and only if
- 读法
- if and only if
- LaTeX
含义
States that two statements imply each other.
示例
数集
Natural numbers
- 读法
- the natural numbers
- LaTeX
含义
The set used for counting numbers. Whether 0 is included depends on convention.
示例
数集
Integers
- 读法
- the integers
- LaTeX
含义
All whole numbers, including negative values, zero, and positive values.
示例
数集
Rational numbers
- 读法
- the rational numbers
- LaTeX
含义
Numbers expressible as a ratio of two integers with nonzero denominator.
示例
数集
Real numbers
- 读法
- the real numbers
- LaTeX
含义
Numbers represented on the continuous number line.
示例
数集
Complex numbers
- 读法
- the complex numbers
- LaTeX
含义
Numbers of the form a+bi, where i is the imaginary unit.
示例
数集
Pi
- 读法
- pi
- LaTeX
含义
The constant ratio of a circle's circumference to its diameter.
示例
微积分与分析
Infinity
- 读法
- infinity
- LaTeX
含义
A symbol for unbounded growth or an unending process, not an ordinary real number.
示例
微积分与分析
Summation
- 读法
- sum
- LaTeX
含义
Adds a sequence of terms over an index range.
示例
微积分与分析
Product notation
- 读法
- product
- LaTeX
含义
Multiplies a sequence of terms over an index range.
示例
微积分与分析
Integral
- 读法
- integral
- LaTeX
含义
Represents accumulation, signed area, or an antiderivative depending on context.
示例
微积分与分析
Partial derivative symbol
- 读法
- partial
- LaTeX
含义
Used when differentiating a multivariable function with respect to one variable.
示例
微积分与分析
Nabla
- 读法
- nabla
- LaTeX
含义
Used for gradient, divergence, curl, and related vector-calculus operations.
示例
代数
Matrix
- 读法
- matrix
- LaTeX
含义
A rectangular arrangement of entries used to represent linear maps, systems, and data.
示例
代数
Transpose
- 读法
- A transpose
- LaTeX
含义
Swaps rows and columns of a matrix.
示例
代数
Inverse matrix
- 读法
- A inverse
- LaTeX
含义
A matrix that multiplies with A to produce the identity matrix, when it exists.
示例
代数
Determinant
- 读法
- determinant of A
- LaTeX
含义
A scalar value that captures scaling, orientation, and invertibility information of a square matrix.
示例
几何
Angle
- 读法
- angle
- LaTeX
含义
Represents an angle formed by two rays or segments.
示例
几何
Degree
- 读法
- degrees
- LaTeX
含义
A unit for measuring angles, where a full turn is 360 degrees.
示例
几何
Perpendicular
- 读法
- is perpendicular to
- LaTeX
含义
Shows that two lines or vectors meet at a right angle.
示例
几何
Parallel
- 读法
- is parallel to
- LaTeX
含义
Shows that two lines or vectors have the same direction and do not meet in a plane.
示例
括号与分隔符
Absolute value
- 读法
- absolute value of x
- LaTeX
含义
The distance of a number from zero on the number line.
示例
括号与分隔符
Floor
- 读法
- floor of x
- LaTeX
含义
The greatest integer less than or equal to x.
示例
括号与分隔符
Ceiling
- 读法
- ceiling of x
- LaTeX
含义
The smallest integer greater than or equal to x.
示例
缩写与标记惯例
End of proof
- 读法
- QED
- LaTeX
含义
Marks the end of a proof. Some texts use Q.E.D. or a filled square.
示例
缩写与标记惯例
Therefore
- 读法
- therefore
- LaTeX
含义
Introduces a conclusion that follows from previous statements.
示例
缩写与标记惯例
Because
- 读法
- because
- LaTeX
含义
Introduces a reason or supporting statement.