Renderer: Native browser MathML · Detection context: math · Dependencies: None

1. Basic Arithmetic

Addition: 2 + 3 = 5

2 + 3 = 5

Multiplication: a × b

a \times b

Division: a ÷ b

a \div b

2. Fractions

Simple fraction: 1/2

\frac{1}{2}

Nested fraction: (a/b) / (c/d)

\frac{\frac{a}{b}}{\frac{c}{d}}

Continued fraction

1 + \frac{1}{2 + \frac{1}{3 + \dots}}

3. Roots

Square root

\sqrt{a^{2} + b^{2}}

Cube root

\sqrt[3]{27}

Nested radical

\sqrt{1 + \sqrt{2 + \sqrt{3}}}

4. Superscripts & Subscripts

Superscript: x²

x^{2}

Subscript: aₙ

a_{n}

Combined: xᵢʲ

x_{i}^{j}

Nested exponent: e^(x²)

e^{x^{2}}

5. Greek Letters & Symbols

Greek alphabet sample

α, β, γ, δ, ε, θ, λ, μ, π, σ, φ, ω

Mathematical symbols

\int, \sum, \prod, \partial, \infty, \in, \forall, \exists, \nabla

6. Summations

Sum of xᵢ from i=1 to n

sum from i equals 1 to n of x sub i

Double sum

\sum_{i = 1}^{m} \sum_{j = 1}^{n} a_{i j}

Product notation

\prod_{k = 1}^{n} a_{k}

7. Integrals

Indefinite integral

\int f (x) d x

Definite integral from a to b

\int_{a}^{b} f (x) d x

Double integral

\int \int f (x, y) d x d y

Contour integral

\oint f (z) d z

8. Limits

Limit as x approaches infinity

lim_{x \to \infty} f (x)

Limit as x approaches 0

lim_{x \to 0} \frac{sin (x)}{x} = 1

9. Matrices

2×2 matrix

[\begin{matrix} a & b \\ c & d \end{matrix}]

3×3 identity matrix

I = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]

Determinant

det (A) = | \begin{matrix} a & b \\ c & d \end{matrix} | = a d - b c

10. Systems of Equations

System of linear equations

{\begin{cases} 2 x + 3 y = 7 \\ x - y = 1 \end{cases}

Piecewise function

f (x) = {\begin{cases} x & if x \geq 0 \\ - x & if x < 0 \end{cases}

11. Calculus

Derivative

\frac{d y}{d x} = f^{'} (x)

Partial derivative

\frac{\partial f}{\partial x}

Gradient

\nabla f = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z})

Divergence

\nabla \cdot \vec{F} = \frac{\partial F_{x}}{\partial x} + \frac{\partial F_{y}}{\partial y} + \frac{\partial F_{z}}{\partial z}

12. Set Notation

Union and intersection

A \cup B, A \cap B

Set-builder notation

{x \in R | x > 0}

Subset and membership

A \subseteq B, x \in A, A ∖ B

13. Logic

Logical operators

p \land q, p \lor q, \neg p

Implication and biconditional

p \Rightarrow q, p \Leftrightarrow q

Quantifiers

\forall x \in S, \exists y : P (x, y)

14. Famous Formulas

Quadratic formula

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Euler's identity

e^{i π} + 1 = 0

Cauchy's integral formula

f (a) = \frac{1}{2 π i} \oint \frac{f (z)}{z - a} d z

Pythagorean theorem

a^{2} + b^{2} = c^{2}

Euler's formula

e^{i θ} = cos θ + i sin θ

Fourier transform

\hat{f} (ξ) = \int_{- \infty}^{\infty} f (x) e^{- 2 π i x ξ} d x

Maxwell's equation (Gauss's law)

\nabla \cdot \vec{E} = \frac{ρ}{ε_{0}}

Navier-Stokes (incompressible)

ρ (\frac{\partial \vec{v}}{\partial t} + \vec{v} \cdot \nabla \vec{v}) = - \nabla p + μ \nabla^{2} \vec{v} + \vec{f}

15. Chemistry-Style Expressions

Water formation

2 H_{2} + O_{2} \to 2 H_{2} O

Photosynthesis

6 {CO}_{2} + 6 H_{2} O \overset{light}{\to} C_{6} H_{12} O_{6} + 6 O_{2}

16. Expressions with Accessibility Attributes

With alttext attribute

{(x + y)}^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) x^{n - k} y^{k}

With aria-label attribute

P (A | B) = \frac{P (B | A) \cdot P (A)}{P (B)}

With both alttext and aria-label

Euler's number e is approximately 2.71828

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Renderer: Native browser MathML · Detection context: math · Dependencies: None

1. Basic Arithmetic

Addition: 2 + 3 = 5

2 + 3 = 5

Multiplication: a × b

a \times b

Division: a ÷ b

a \div b

2. Fractions

Simple fraction: 1/2

\frac{1}{2}

Nested fraction: (a/b) / (c/d)

\frac{\frac{a}{b}}{\frac{c}{d}}

Continued fraction

1 + \frac{1}{2 + \frac{1}{3 + \dots}}

3. Roots

Square root

\sqrt{a^{2} + b^{2}}

Cube root

\sqrt[3]{27}

Nested radical

\sqrt{1 + \sqrt{2 + \sqrt{3}}}

4. Superscripts & Subscripts

Superscript: x²

x^{2}

Subscript: aₙ

a_{n}

Combined: xᵢʲ

x_{i}^{j}

Nested exponent: e^(x²)

e^{x^{2}}

5. Greek Letters & Symbols

Greek alphabet sample

α, β, γ, δ, ε, θ, λ, μ, π, σ, φ, ω

Mathematical symbols

\int, \sum, \prod, \partial, \infty, \in, \forall, \exists, \nabla

6. Summations

Sum of xᵢ from i=1 to n

sum from i equals 1 to n of x sub i

Double sum

\sum_{i = 1}^{m} \sum_{j = 1}^{n} a_{i j}

Product notation

\prod_{k = 1}^{n} a_{k}

7. Integrals

Indefinite integral

\int f (x) d x

Definite integral from a to b

\int_{a}^{b} f (x) d x

Double integral

\int \int f (x, y) d x d y

Contour integral

\oint f (z) d z

8. Limits

Limit as x approaches infinity

lim_{x \to \infty} f (x)

Limit as x approaches 0

lim_{x \to 0} \frac{sin (x)}{x} = 1

9. Matrices

2×2 matrix

[\begin{matrix} a & b \\ c & d \end{matrix}]

3×3 identity matrix

I = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]

Determinant

det (A) = | \begin{matrix} a & b \\ c & d \end{matrix} | = a d - b c

10. Systems of Equations

System of linear equations

{\begin{cases} 2 x + 3 y = 7 \\ x - y = 1 \end{cases}

Piecewise function

f (x) = {\begin{cases} x & if x \geq 0 \\ - x & if x < 0 \end{cases}

11. Calculus

Derivative

\frac{d y}{d x} = f^{'} (x)

Partial derivative

\frac{\partial f}{\partial x}

Gradient

\nabla f = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z})

Divergence

\nabla \cdot \vec{F} = \frac{\partial F_{x}}{\partial x} + \frac{\partial F_{y}}{\partial y} + \frac{\partial F_{z}}{\partial z}

12. Set Notation

Union and intersection

A \cup B, A \cap B

Set-builder notation

{x \in R | x > 0}

Subset and membership

A \subseteq B, x \in A, A ∖ B

13. Logic

Logical operators

p \land q, p \lor q, \neg p

Implication and biconditional

p \Rightarrow q, p \Leftrightarrow q

Quantifiers

\forall x \in S, \exists y : P (x, y)

14. Famous Formulas

Quadratic formula

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Euler's identity

e^{i π} + 1 = 0

Cauchy's integral formula

f (a) = \frac{1}{2 π i} \oint \frac{f (z)}{z - a} d z

Pythagorean theorem

a^{2} + b^{2} = c^{2}

Euler's formula

e^{i θ} = cos θ + i sin θ

Fourier transform

\hat{f} (ξ) = \int_{- \infty}^{\infty} f (x) e^{- 2 π i x ξ} d x

Maxwell's equation (Gauss's law)

\nabla \cdot \vec{E} = \frac{ρ}{ε_{0}}

Navier-Stokes (incompressible)

ρ (\frac{\partial \vec{v}}{\partial t} + \vec{v} \cdot \nabla \vec{v}) = - \nabla p + μ \nabla^{2} \vec{v} + \vec{f}

15. Chemistry-Style Expressions

Water formation

2 H_{2} + O_{2} \to 2 H_{2} O

Photosynthesis

6 {CO}_{2} + 6 H_{2} O \overset{light}{\to} C_{6} H_{12} O_{6} + 6 O_{2}

16. Expressions with Accessibility Attributes

With alttext attribute

{(x + y)}^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) x^{n - k} y^{k}

With aria-label attribute

P (A | B) = \frac{P (B | A) \cdot P (A)}{P (B)}

With both alttext and aria-label

Euler's number e is approximately 2.71828

Native MathML Samples

1. Basic Arithmetic

2. Fractions

3. Roots

4. Superscripts & Subscripts

5. Greek Letters & Symbols

6. Summations

7. Integrals

8. Limits

9. Matrices

10. Systems of Equations

11. Calculus

12. Set Notation

13. Logic

14. Famous Formulas

15. Chemistry-Style Expressions

16. Expressions with Accessibility Attributes

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Native MathML Samples

1. Basic Arithmetic

2. Fractions

3. Roots

4. Superscripts & Subscripts

5. Greek Letters & Symbols

6. Summations

7. Integrals

8. Limits

9. Matrices

10. Systems of Equations

11. Calculus

12. Set Notation

13. Logic

14. Famous Formulas

15. Chemistry-Style Expressions

16. Expressions with Accessibility Attributes