This article will help you better understand many symbols in mathematics. Welcome aboard!
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1. THE PLUS SIGN\TEXT{1.~THE~PLUS~SIGN}1. THE PLUS SIGN
Plus Sign — the most fundamental and frequently used operator in mathematics. It originated from the Latin word etetet ("and") and was introduced to print by European mathematicians around the 151515th 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=83 + 5 = 83+5=8 (basic addition)
* Algebra: x+2=7x + 2 = 7x+2=7 (combining terms in an equation)
* Vectors: (1,2)+(3,4)=(4,6)(1, 2) + (3, 4) = (4, 6)(1,2)+(3,4)=(4,6) (component-wise addition)
* Set Theory: A+BA + BA+B (disjoint union — merging sets with no overlapping elements)
* Programming (For example about Python): Hello + World → HelloWorld (string concatenation)
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2. THE MINUS SIGN\TEXT{2.~THE~MINUS~SIGN}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 151515th-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., set111 - set222).
For example
* Arithmetic: 10−4=610 - 4 = 610−4=6 (basic subtraction)
* Algebra: x−3=5x - 3 = 5x−3=5 (rearranging terms)
* Vectors: (5,7)−(2,3)=(3,4)(5, 7) - (2, 3) = (3, 4)(5,7)−(2,3)=(3,4) (component-wise subtraction)
* Set Theory: A−BA - BA−B (set difference — elements in AAA but not in BBB)
* Programming (For example about Python): HelloWorld - World → not supported (strings don't support subtraction, but lists do)
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3. THE MULTIPLICATION SIGN\TEXT{3.~THE~MULTIPLICATION~SIGN}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 163116311631, 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=244 × 6 = 244×6=24 (444 groups of 666)
* Algebra: 3x ⋅ 2y=6xy3x~·~2y = 6xy3x ⋅ 2y=6xy (multiplying coefficients and variables)
* Linear Algebra: matrix multiplication A⋅BA · BA⋅B (row-by-column summation)
* Set Theory: Cartesian product A×BA × BA×B (all ordered pairs from two sets)
* Programming (For example about Python): 3∗4=123 * 4 = 123∗4=12 (numeric multiplication), ha * 333 → hahaha (string repetition)
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4. THE DIVISION SIGN\TEXT{4.~THE~DIVISION~SIGN}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 165916591659, derived from Latin divisio (division); / (slash) was popularized by De Morgan and others in the 191919th 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=520 ÷ 4 = 520÷4=5 (partitioning 202020 into 444 equal parts)
* Fraction: 1/2 (111 divided by 222, or one half)
* Algebra: (x2−4)/(x−2)=x+2(x² - 4) / (x - 2) = x + 2(x2−4)/(x−2)=x+2 (polynomial division simplification)
* Ratio: 3:23 : 23:2 (333 to 222, equivalent to 3/23/23/2)
* Programming (For example about Python): 10/3=3.333...10 / 3 = 3.333...10/3=3.333... (float division), 10//3=310 // 3 = 310//3=3 (integer division)
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5. THE SIGMA SIGN\TEXT{5.~THE SIGMA~SIGN}5. THE SIGMA SIGN
Summation Sign — the core symbol for "repeated addition of a sequence." It originates from the Greek capital letter Sigma (σσσ) and was popularized by Swiss mathematician Euler in the 181818th 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=15i=1+2+3+4+5=15∑_{i=1}^{5} i = 1 + 2 + 3 + 4 + 5 = 15∑i=15 i=1+2+3+4+5=15 (sum from 111 to 555)
* Algebra: ∑k=1nk2=12+22+...+n2∑_{k=1}^{n} k² = 1² + 2² + ... + n²∑k=1n k2=12+22+...+n2 (sum of first nnn squares)
* Statistics: ∑i=1nxi∑_{i=1}^{n} x_i∑i=1n xi (sum of nnn data points, used for calculating the mean)
* Calculus Prerequisite: ∑i=1nf(xi)Δx∑_{i=1}^{n} f(x_i) Δx∑i=1n f(xi )Δx (Riemann sum, discrete approximation of an integral)
* Programming (For example about Python): sum(range(1, 6)) = 151515 (built-in sum), np.sum(arr) (NumPy array summation)
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> Other signs will be join in tomorrow！
