Algebraic Notation
Algebraic notation describes how algebra is written. It follows certain rules and conventions, and has its own terminology. For example, the expression has the following components:
1 – Exponent (power), 2 – Coefficient, 3 – term, 4 – operator, 5 – constant, – variables
A coefficient is a numerical value which multiplies a variable (the operator is omitted). A term is an addend or a summand, a group of coefficients, variables, constants and exponents that may be separated from the other terms by the plus and minus operators. Letters represent variables and constants. By convention, letters at the beginning of the alphabet (e.g. ) are typically used to represent constants, and those toward the end of the alphabet (e.g. and ) are used to represent variables. They are usually written in italics.
Algebraic operations work in the same way as arithmetic operations, such as addition, subtraction, multiplication, division and exponentiation. and are applied to algebraic variables and terms. Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a coefficient is used. For example, is written as, and may be written .
Usually terms with the highest power (exponent), are written on the left, for example, is written to the left of . When a coefficient is one, it is usually omitted (e.g. is written ). Likewise when the exponent (power) is one, (e.g. is written ). When the exponent is zero, the result is always 1 (e.g. is always rewritten to ). However, being undefined, should not appear in an expression, and care should be taken in simplifying expressions in which variables may appear in exponents.
Read more about this topic: Elementary Algebra
Famous quotes containing the word algebraic:
“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)