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If an expression can be evaluated by straightforward application of simple techniques and without recourse to extended calculation or general theory, then it can be evaluated by inspection. It is also applied to solving equations; for example to find roots of a quadratic equation by inspection is to 'notice' them, or mentally check them.
The same syntactic expression 1 + 2 × 3 can have different values (mathematically 7, but also 9), depending on the order of operations implied by the context (See also Operations § Calculators). For real numbers , the product a × b × c {\displaystyle a\times b\times c} is unambiguous because ( a × b ) × c = a × ( b × c ) {\displaystyle ...
The acronym's procedural application does not match experts' intuitive understanding of mathematical notation: mathematical notation indicates groupings in ways other than parentheses or brackets and a mathematical expression is a tree-like hierarchy rather than a linearly "ordered" structure; furthermore, there is no single order by which ...
This is not possible here, as there is no natural order on symbols, and many symbols are used in different parts of mathematics with different meanings, often completely unrelated. Therefore, some arbitrary choices had to be made, which are summarized below. The article is split into sections that are sorted by an increasing level of technicality.
Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients.. Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer.
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
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