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1 Comprehensive List of Mathematical Symbols Comprehensive List of Mathematical Symbols Comprehensive List of Mathematical Symbols For the corresponding web guides, see Mathematical Symbols. Table of Contents 1 Constant .. 3. Key Mathematical Numbers .. 3. Key Mathematical Sets .. 4. Key Mathematical Infinities .. 5. Other Key Mathematical Objects .. 6. 2 Variables .. 6. Variables for Numbers .. 6. Variables in Geometry .. 7. Variables in Calculus .. 7. Variables in Linear Algebra .. 8. Variables in Set Theory and Logic .. 8. Variables in Probability and Statistics .. 9. 3 Delimiters .. 10. Common Delimiters.

2 10. Other Delimiters .. 10. 4 Operators .. 11. 2 Table of Contents Comprehensive List of Mathematical Symbols Common Operators .. 11. Function-related Operators .. 12. Elementary Functions .. 12. Algebra-related Operators .. 13. Geometry-related Operators .. 14. Logic-related Operators .. 15. Set-related Operators .. 16. Vector-related Operators .. 16. Matrix-related Operators .. 17. Probability-related Operators .. 18. Statistics-related Operators .. 18. Key Probability Functions and Distributions .. 19. Calculus-related Operators .. 20. 5 Relational Symbols .. 21. Equality-based Relational Symbols.

3 21. Comparison-based Relational Symbols .. 21. Number-related Relational Symbols .. 22. Geometry-related Relational Symbols .. 22. Set-related Relational Symbols .. 22. Logic-related Relational Symbols .. 23. Probability-related Relational Symbols .. 23. Calculus-related Relational Symbols .. 24. 6 Notational Symbols .. 24. Common Notational Symbols .. 24. Notational Symbols in Geometry and Trigonom- etry .. 25. Notational Symbols in Calculus .. 25. Notational Symbols in Probability and Statistics 26. 7 Additional Resources .. 26. 1 Constant Key Mathematical Numbers Key Mathematical Numbers 3.

4 Comprehensive List of Mathematical Symbols Symbols LaTeX Code Example (Explanation). 0 $0$ 3+0=3. (Zero, additive identity). 1 $1$ 5 1=5. (One, multiplicative identity).. 2 $\sqrt{2}$ ( 2 + 1)2 = 3 + 2 2. (Square root of 2). e $e$ ln(e2 ) = 2. (Euler's constant). 2 1 1. $\pi$ = 2 + 2 + . (Pi, Archimedes' 6 1 2. constant).. 1+ 5. $\varphi$ =. (Phi, golden ratio) 2. i $i$ (1 + i)2 = 2i (Imaginary unit). Key Mathematical Sets Symbols LaTeX Code Example (Explanation). $\varnothing$ | | = 0. (Empty set). N $\mathbb{N}$ x, y N, x + y N. (Set of natural numbers). Z $\mathbb{Z}$ N Z. (Set of integers).

5 4 Key Mathematical Sets Comprehensive List of Mathematical Symbols Z+ $\mathbb{Z}_+$ 3 Z+. (Set of positive integers).. Q $\mathbb{Q}$ 2 . /Q. (Set of rational numbers). R $\mathbb{R}$ x R (x2 0). (Set of real numbers). R+ $\mathbb{R}_+$ x, y R+ (xy R+ ). (Set of positive real numbers). C $\mathbb{C}$ z C (z 2 + 1 = 0). (Set of complex numbers). Zn $\mathbb{Z}_n$ In the world of Z2 , (Set of integer modulo 1 + 1 = 0. n). R3 $\mathbb{R}^3$ (5, 1, 2) R3. (Three-dimensional Euclidean space). Key Mathematical Infinities Symbols LaTeX Code Example (Explanation). 0 $\aleph_0$ 0 + 5 = 0. (Cardinality of natural numbers).

6 C $\mathfrak{c}$ c = 2 0. (Cardinality of real numbers). $\omega$ n N (n < ). (Smallest infinite ordinal number). Key Mathematical Infinities 5. Comprehensive List of Mathematical Symbols Other Key Mathematical Objects Symbols LaTeX Code Example (Explanation). 0 $\mathbf{0}$ v V, v + 0 = v (Zero vector). e $e$ e e=e (Identity element of a group). I $I$ AI = IA = A. (Identity matrix). Z. C $C$ 1 dx = x + C. (Constant of integration). > $\top$ For each proposition P , (Tautology) P > P. $\bot$ For each proposition P , (Contradiction) P P . Z $Z$ Z N (0, 1). (Standard normal distribution). 2 Variables Variables for Numbers Symbols LaTeX Code Example (Explanation).

7 M, n, p, q $m$, $n$, $p$, $q$ m+n q =1. (Integers and natural numbers). 6 Variables for Numbers Comprehensive List of Mathematical Symbols a, b, c $a$, $b$, $c$ ax + by = 0. (Coefficients for functions and equations). x, y, z $x$, $y$, $z$ If 2x + 5 = 3, then (Unknowns in x = 1. functions and equations). $\Delta$ = b2 4ac for (Discriminant) quadratic polynomials X. 10. i, j, k $i$, $j$, $k$ i = 55. (Index variables) i=1. t $t$ At t = 5, the velocity (Time variable) is v(5) = 32. z $z$ z z = |z|2. (Complex numbers). Variables in Geometry Symbols LaTeX Code Example (Explanation). P , Q, R, S $P$, $Q$, $R$, $S$ P Q QR.

8 (Vertices). $\ell$ 1 k 2. (Lines). , , , $\alpha$, $\beta$, + + = 180 . (Angles) $\gamma$, $\theta$. Variables in Calculus Symbols LaTeX Code Example (Explanation). Variables in Calculus 7. Comprehensive List of Mathematical Symbols f (x), g(x, y), h(z) $f(x)$, $g(x,y)$, f (2) = g(3, 1) + 5. (Functions) $h(z)$. 3. an , bn , cn $a_n$, $b_n$, an =. (Sequences) $c_n$ n+2. eh e0. h, x $h$, $\Delta x$ lim =1. (Limiting variables in h 0 h derivatives). , $\delta$, For all > 0, there is a (Small quantities in $\varepsilon$ > 0 such that |x| < . proofs involving implies that |2x| < . limits). F (x), G(x) $F(x)$, $G(x)$ F 0 (x) = f (x).

9 (Antiderivatives). Variables in Linear Algebra Symbols LaTeX Code Example (Explanation). u, v, w $\mathbf{u}$, 3u + 4v = w (Vectors) $\mathbf{v}$, $\mathbf{w}$. A, B, C $A$, $B$, $C$ AX = B. (Matrices). $\lambda$ Av = v (Eigenvalues). Variables in Set Theory and Logic Symbols LaTeX Code Example (Explanation). A, B, C $A$, $B$, $C$ A B C. (Sets). 8 Variables in Set Theory and Logic Comprehensive List of Mathematical Symbols a, b, c $a$, $b$, $c$ a A. (Elements). P , Q, R $P$, $Q$, $R$ P P >. (Propositions). Variables in Probability and Statistics Symbols LaTeX Code Example (Explanation). X, Y , Z $X$, $Y$, $Z$ E(X + Y ) =.

10 (Random variables) E(X) + E(Y ). $\mu$ H0 : = 5. (Population means). $\sigma$ 1 = 2. (Population standard deviations). s $s$ s 6= . (Sample standard deviations). n $n$ For n 30, use the (Sample sizes) normal distribution. $\rho$ Ha : < 0. (Population correlations). r $r$ If r = , then (Sample correlations) r2 = $\pi$ = (Population proportions). X. p $p$ p=. (Sample proportions) n Variables in Probability and Statistics 9. Comprehensive List of Mathematical Symbols 3 Delimiters Common Delimiters Symbols LaTeX Code Example (Explanation).. $.$ (Decimal separator). : $:$ 1 : 4 : 9 = 3 : 12 : 27.