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Référence

Guide des symboles mathématiques

Une référence pratique pour les symboles mathématiques courants, avec des lectures, des commandes LaTeX, des exemples et des idées d'invites IA.

Opérations de base

Plus

Lu comme
plus
LaTeX

Signification

Adds two quantities.

Exemple

3+5=83+5=8

Opérations de base

Minus

Lu comme
minus
LaTeX

Signification

Subtracts one quantity from another, or marks a negative value.

Exemple

9−4=59-4=5

Opérations de base

Multiplication sign

Lu comme
times
LaTeX

Signification

Multiplies two quantities. In algebra, multiplication is often written with a dot or omitted.

Exemple

7×8=567\times 8=56

Opérations de base

Division sign

Lu comme
divided by
LaTeX

Signification

Divides one quantity by another nonzero quantity.

Exemple

12÷4=312\div 4=3

Opérations de base

Fraction

Lu comme
a over b
LaTeX

Signification

Represents division or a ratio with a numerator and denominator.

Exemple

36=12\frac{3}{6}=\frac{1}{2}

Opérations de base

Plus-minus

Lu comme
plus or minus
LaTeX

Signification

Indicates that both the positive and negative alternatives are being considered.

Exemple

10±3=13 or 710\pm 3=13\text{ or }7

Opérations de base

Square root

Lu comme
square root of x
LaTeX

Signification

The nonnegative value whose square is x, unless a different convention is stated.

Exemple

9=3\sqrt{9}=3

Relations

Equals

Lu comme
equals
LaTeX

Signification

States that two expressions have the same value or represent the same object.

Exemple

2+3=52+3=5

Relations

Not equal

Lu comme
is not equal to
LaTeX

Signification

Shows that two expressions do not have the same value.

Exemple

4≠54\ne 5

Relations

Approximately equal

Lu comme
approximately equal to
LaTeX

Signification

Indicates a rounded or approximate value rather than exact equality.

Exemple

π≈3.14\pi\approx 3.14

Relations

Less than or equal to

Lu comme
less than or equal to
LaTeX

Signification

Allows equality while comparing two quantities.

Exemple

x≤10x\le 10

Relations

Greater than or equal to

Lu comme
greater than or equal to
LaTeX

Signification

Compares two quantities while allowing equality.

Exemple

x≥0x\ge 0

Relations

Proportional to

Lu comme
is proportional to
LaTeX

Signification

Shows that one quantity changes by a constant multiple of another.

Exemple

y∝xy\propto x

Théorie des ensembles

Empty set

Lu comme
empty set
LaTeX

Signification

The set with no elements.

Exemple

{1}∩{2}=∅\{1\}\cap\{2\}=\emptyset

Théorie des ensembles

Element of

Lu comme
is an element of
LaTeX

Signification

Shows that a value belongs to a set.

Exemple

3∈{1,2,3}3\in\{1,2,3\}

Théorie des ensembles

Not an element of

Lu comme
is not an element of
LaTeX

Signification

Shows that a value does not belong to a set.

Exemple

4∉{1,2,3}4\notin\{1,2,3\}

Théorie des ensembles

Proper subset

Lu comme
is a proper subset of
LaTeX

Signification

Usually indicates that every element of one set is in another, and the two sets are not equal.

Exemple

{1,2}⊂{1,2,3}\{1,2\}\subset\{1,2,3\}

Théorie des ensembles

Subset or equal

Lu comme
is a subset of or equal to
LaTeX

Signification

Allows two sets to be equal while stating subset inclusion.

Exemple

{1,2}⊆{1,2}\{1,2\}\subseteq\{1,2\}

Théorie des ensembles

Union

Lu comme
union
LaTeX

Signification

Combines all elements that are in either set.

Exemple

{1,2}∪{2,3}={1,2,3}\{1,2\}\cup\{2,3\}=\{1,2,3\}

Théorie des ensembles

Intersection

Lu comme
intersection
LaTeX

Signification

Keeps only the elements shared by both sets.

Exemple

{1,2}∩{2,3}={2}\{1,2\}\cap\{2,3\}=\{2\}

Logique

Universal quantifier

Lu comme
for all
LaTeX

Signification

States that a claim applies to every object in a domain.

Exemple

∀x∈R, x2≥0\forall x\in\mathbb{R},\ x^2\ge 0

Logique

Existential quantifier

Lu comme
there exists
LaTeX

Signification

States that at least one object satisfying a condition exists.

Exemple

∃x∈R:x2=4\exists x\in\mathbb{R}: x^2=4

Logique

Negation

Lu comme
not
LaTeX

Signification

Reverses the truth value of a statement.

Exemple

¬P\neg P

Logique

Logical and

Lu comme
and
LaTeX

Signification

True only when both connected statements are true.

Exemple

P∧QP\land Q

Logique

Logical or

Lu comme
or
LaTeX

Signification

True when at least one connected statement is true.

Exemple

P∨QP\lor Q

Logique

Implication

Lu comme
implies
LaTeX

Signification

Connects a condition to a conclusion.

Exemple

x>2⇒x2>4x>2\Rightarrow x^2>4

Logique

If and only if

Lu comme
if and only if
LaTeX

Signification

States that two statements imply each other.

Exemple

x2=1⇔x=±1x^2=1\Leftrightarrow x=\pm 1

Ensembles de nombres

Natural numbers

Lu comme
the natural numbers
LaTeX

Signification

The set used for counting numbers. Whether 0 is included depends on convention.

Exemple

n∈Nn\in\mathbb{N}

Ensembles de nombres

Integers

Lu comme
the integers
LaTeX

Signification

All whole numbers, including negative values, zero, and positive values.

Exemple

−3∈Z-3\in\mathbb{Z}

Ensembles de nombres

Rational numbers

Lu comme
the rational numbers
LaTeX

Signification

Numbers expressible as a ratio of two integers with nonzero denominator.

Exemple

23∈Q\frac{2}{3}\in\mathbb{Q}

Ensembles de nombres

Real numbers

Lu comme
the real numbers
LaTeX

Signification

Numbers represented on the continuous number line.

Exemple

2∈R\sqrt{2}\in\mathbb{R}

Ensembles de nombres

Complex numbers

Lu comme
the complex numbers
LaTeX

Signification

Numbers of the form a+bi, where i is the imaginary unit.

Exemple

3+2i∈C3+2i\in\mathbb{C}

Ensembles de nombres

Pi

Lu comme
pi
LaTeX

Signification

The constant ratio of a circle's circumference to its diameter.

Exemple

A=πr2A=\pi r^2

Calcul et analyse

Infinity

Lu comme
infinity
LaTeX

Signification

A symbol for unbounded growth or an unending process, not an ordinary real number.

Exemple

lim⁡x→∞1x=0\lim_{x\to\infty}\frac{1}{x}=0

Calcul et analyse

Summation

Lu comme
sum
LaTeX

Signification

Adds a sequence of terms over an index range.

Exemple

∑k=14k2=30\sum_{k=1}^{4}k^2=30

Calcul et analyse

Product notation

Lu comme
product
LaTeX

Signification

Multiplies a sequence of terms over an index range.

Exemple

∏k=14k=24\prod_{k=1}^{4}k=24

Calcul et analyse

Integral

Lu comme
integral
LaTeX

Signification

Represents accumulation, signed area, or an antiderivative depending on context.

Exemple

∫01x2 dx=13\int_0^1 x^2\,dx=\frac{1}{3}

Calcul et analyse

Partial derivative symbol

Lu comme
partial
LaTeX

Signification

Used when differentiating a multivariable function with respect to one variable.

Exemple

∂f∂x\frac{\partial f}{\partial x}

Calcul et analyse

Nabla

Lu comme
nabla
LaTeX

Signification

Used for gradient, divergence, curl, and related vector-calculus operations.

Exemple

∇f\nabla f

Algèbre

Matrix

Lu comme
matrix
LaTeX

Signification

A rectangular arrangement of entries used to represent linear maps, systems, and data.

Exemple

[1234]\begin{bmatrix}1&2\\3&4\end{bmatrix}

Algèbre

Transpose

Lu comme
A transpose
LaTeX

Signification

Swaps rows and columns of a matrix.

Exemple

[1234]T=[1324]\begin{bmatrix}1&2\\3&4\end{bmatrix}^T=\begin{bmatrix}1&3\\2&4\end{bmatrix}

Algèbre

Inverse matrix

Lu comme
A inverse
LaTeX

Signification

A matrix that multiplies with A to produce the identity matrix, when it exists.

Exemple

AA−1=IAA^{-1}=I

Algèbre

Determinant

Lu comme
determinant of A
LaTeX

Signification

A scalar value that captures scaling, orientation, and invertibility information of a square matrix.

Exemple

det⁡[abcd]=ad−bc\det\begin{bmatrix}a&b\\c&d\end{bmatrix}=ad-bc

Géométrie

Angle

Lu comme
angle
LaTeX

Signification

Represents an angle formed by two rays or segments.

Exemple

∠ABC=60∘\angle ABC=60^\circ

Géométrie

Degree

Lu comme
degrees
LaTeX

Signification

A unit for measuring angles, where a full turn is 360 degrees.

Exemple

90∘90^\circ

Géométrie

Perpendicular

Lu comme
is perpendicular to
LaTeX

Signification

Shows that two lines or vectors meet at a right angle.

Exemple

AB⊥CDAB\perp CD

Géométrie

Parallel

Lu comme
is parallel to
LaTeX

Signification

Shows that two lines or vectors have the same direction and do not meet in a plane.

Exemple

AB∥CDAB\parallel CD

Parenthèses et délimiteurs

Absolute value

Lu comme
absolute value of x
LaTeX

Signification

The distance of a number from zero on the number line.

Exemple

∣−3∣=3|-3|=3

Parenthèses et délimiteurs

Floor

Lu comme
floor of x
LaTeX

Signification

The greatest integer less than or equal to x.

Exemple

⌊3.8⌋=3\lfloor 3.8\rfloor=3

Parenthèses et délimiteurs

Ceiling

Lu comme
ceiling of x
LaTeX

Signification

The smallest integer greater than or equal to x.

Exemple

⌈3.2⌉=4\lceil 3.2\rceil=4

Abréviations

End of proof

Lu comme
QED
LaTeX

Signification

Marks the end of a proof. Some texts use Q.E.D. or a filled square.

Exemple

∴x=1.□\therefore x=1.\quad\square

Abréviations

Therefore

Lu comme
therefore
LaTeX

Signification

Introduces a conclusion that follows from previous statements.

Exemple

a=b, b=c ∴a=ca=b,\ b=c\ \therefore a=c

Abréviations

Because

Lu comme
because
LaTeX

Signification

Introduces a reason or supporting statement.

Exemple

∵x>0\because x>0

Lectures complémentaires

Ces liens sont fournis comme lecture supplémentaire. Les explications et exemples de cette page sont rédigés pour ce site.