Math Symbols List

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2026-10-10 23:31:59

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This article will help you better understand many symbols in mathematics. Welcome aboard!

$\text{1.~The~Plus~Sign}$

Plus Sign — the most fundamental and frequently used operator in mathematics. It originated from the Latin word $et$ ("and") and was introduced to print by European mathematicians around the $15$ th century, eventually becoming the standard symbol for "combination" and "increase." In arithmetic, the plus sign denotes the addition of two or more quantities and serves as the starting point of the four basic operations. In algebra, the positive sign "+" marks positive numbers or vector addition. In set theory, "+" can denote disjoint union. In programming, + is used not only for numeric addition but also for string concatenation.

For example

Arithmetic: $3 + 5 = 8$ (basic addition)
Algebra: $x + 2 = 7$ (combining terms in an equation)
Vectors: $(1, 2) + (3, 4) = (4, 6)$ (component-wise addition)
Set Theory: $A + B$ (disjoint union — merging sets with no overlapping elements)
Programming (For example about Python): Hello + World → HelloWorld (string concatenation)

$\text{2.~The~Minus~Sign}$

Minus Sign — the second most fundamental operator in mathematics, sharing its origin with the plus sign. It was introduced to print in $15$ th-century Europe and represents "removal, decrease, and reversal" — the inverse of addition. In arithmetic, it denotes subtracting one quantity from another. In algebra, the negative sign marks negative numbers or subtraction operations. In vectors, it means component-wise subtraction. In programming, - is used for numeric subtraction and, in some languages, set difference (e.g., set $1$ - set $2$ ).

For example

Arithmetic: $10 - 4 = 6$ (basic subtraction)
Algebra: $x - 3 = 5$ (rearranging terms)
Vectors: $(5, 7) - (2, 3) = (3, 4)$ (component-wise subtraction)
Set Theory: $A - B$ (set difference — elements in $A$ but not in $B$ )
Programming (For example about Python): HelloWorld - World → not supported (strings don't support subtraction, but lists do)

$\text{3.~The~Multiplication~Sign}$

Multiplication Sign — the core operator for "repeated addition, scaling, and combination." Historically, multiple forms exist: × was introduced by English mathematician William Oughtred in $1631$ , derived from Latin crux (cross); · (middle dot) was popularized by Leibniz to avoid confusion with the letter x; * is widely used in programming. Multiplication is a shortcut for repeated addition, with distinct meanings in algebra, linear algebra, set theory, and programming.

For example

Arithmetic: $4 × 6 = 24$ ( $4$ groups of $6$ )
Algebra: $3x~·~2y = 6xy$ (multiplying coefficients and variables)
Linear Algebra: matrix multiplication $A · B$ (row-by-column summation)
Set Theory: Cartesian product $A × B$ (all ordered pairs from two sets)
Programming (For example about Python): $3 * 4 = 12$ (numeric multiplication), ha * $3$ → hahaha (string repetition)

$\text{4.~The~Division~Sign}$

Division Sign — the operator for "partition, ratio, and inverse multiplication." ÷ (obelus) was first introduced by Swiss mathematician Johann Heinrich Rahn in $1659$ , derived from Latin divisio (division); / (slash) was popularized by De Morgan and others in the $19$ th century and is now the standard in programming and typesetting; : (colon) is commonly used for ratios in continental Europe. Division is the inverse of multiplication, with distinct forms in arithmetic, fractions, algebra, set theory, and programming.

For example

Arithmetic: $20 ÷ 4 = 5$ (partitioning $20$ into $4$ equal parts)
Fraction: 1/2 ( $1$ divided by $2$ , or one half)
Algebra: $(x² - 4) / (x - 2) = x + 2$ (polynomial division simplification)
Ratio: $3 : 2$ ( $3$ to $2$ , equivalent to $3/2$ )
Programming (For example about Python): $10 / 3 = 3.333...$ (float division), $10 // 3 = 3$ (integer division)

$\text{5.~The Sigma~Sign}$

Summation Sign — the core symbol for "repeated addition of a sequence." It originates from the Greek capital letter Sigma ( $σ$ ) and was popularized by Swiss mathematician Euler in the $18$ th century. $∑$ denotes the consecutive addition of a series of numbers following a pattern, and is indispensable in calculus, discrete mathematics, statistics, and programming. It compresses "writing plus signs a hundred times" into one compact expression.

For example

Arithmetic: $∑_{i=1}^{5} i = 1 + 2 + 3 + 4 + 5 = 15$ (sum from $1$ to $5$ )
Algebra: $∑_{k=1}^{n} k² = 1² + 2² + ... + n²$ (sum of first $n$ squares)
Statistics: $∑_{i=1}^{n} x_i$ (sum of $n$ data points, used for calculating the mean)
Calculus Prerequisite: $∑_{i=1}^{n} f(x_i) Δx$ (Riemann sum, discrete approximation of an integral)
Programming (For example about Python): sum(range(1, 6)) = $15$ (built-in sum), np.sum(arr) (NumPy array summation)