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For example, + is an algebraic expression. Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression: + An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions.
The plus–minus sign, ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign. For example, y = x ± 1 represents the two equations y = x + 1 and y = x − 1. Sometimes, it is used for denoting a positive-or-negative term such as ±x.
√ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of. For example, +. 2.
A – adele ring or algebraic numbers. a.a.s. – asymptotically almost surely. AC – Axiom of Choice, [1] or set of absolutely continuous functions. a.c. – absolutely continuous. acrd – inverse chord function. ad – adjoint representation (or adjoint action) of a Lie group. adj – adjugate of a matrix. a.e. – almost everywhere.
A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
For example, "almost all real numbers are transcendental" because the algebraic real numbers form a countable subset of the real numbers with measure zero. One can also speak of "almost all" integers having a property to mean "all except finitely many", despite the integers not admitting a measure for which this agrees with the previous usage.