Mathematical Symbols
Symbols play a key role in mathematics. They indicate sign (positive or negative) and grouping, describe operations and relationships, and represent numbers, shapes, constants, and variables in equations. The most basic type of mathematical symbol is a numeral, which is a symbol for a number. Ancient cultures used many different symbols to represent numbers. The numerals used today for the cardinal numbers (1,2,3...) are traced to Hindu and Arabic sources. The Egyptians, Babylonians, and Romans used different symbols, for example, the Hindu-Arabic numeral 10 is represented by X in Roman notation.
Although the exact origin of some mathematical symbols is not known, many were derived from the Arabic, Latin, and Greek languages and first appeared in print in Europe during the fifteenth through the seventeenth centuries. For example, the plus sign, +, is thought to originate from the Latin word et which means "and" in English. Its mathematical use has been found in manuscripts dating back to the 1400s.
The introduction or popularization of some symbols can be traced to specific mathematicians. Robert Recorde is credited with popularizing the use of two parallel lines, =, to indicate an equivalent relationship between mathematical terms. He first used this symbol in print in 1557. The common use of the letters x, y, and z to represent unknown variables in algebraic equations is attributed to Renée Descartes (1596-1650). Leonhard Euler (1707-1783) is often credited for the use of e for the base of natural logarithms, r for the radius of a circle, i for an imaginary number, f(x) for a function of x, for summation, and for finite difference.
The latter two symbols, and , are letters from the Greek alphabet. Greek letters are widely used in mathematics, physics, engineering and other sciences to represent variables and constants. In mathematics, is an example of additive notation and indicates that a series is to be added. For example, xi for i=1 to 3 means the summation of x1, x2, and x3 or x1+ x2+x3. represents a difference between values. For example, if T1=50 and T2=30 then T=50-30=20. Sometimes upper and lower case versions of Greek letters have different meanings. For example, the lower case letter pi, , represents the ratio of the circumference of a circle to its diameter. However, an upper case pi, P, is a multiplicative notation that represents series multiplication, e.g., Pxi for i=1 to 3 means the product of x1, x2, and x3 or x1x x2xx3.
Note that multiplication can also be represented by a raised dot, as in x1·x2·x3, by an asterisk, as in x1* x2*x3, using parentheses to show grouping, as in (x1)(x2)(x3), or by juxtaposition of the terms with no symbol, as in x1x2x3. Throughout history, mathematicians often used different symbols to represent the same concept. For example, Leonhard Euler and Johann Bernoulli used p and c, respectively, to represent at various times in their writings. Certain symbols became popular over time, while others did not. Today there is a general consensus about symbols that are widely used in various branches of mathematics. These symbols are shown below along with their meanings:
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