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Examples include: Simplification of algebraic expressions, in computer algebra; Simplification of boolean expressions i.e. logic optimization; Simplification by conjunction elimination in inference in logic yields a simpler, but generally non-equivalent formula; Simplification of fractions
For example, is an expression, while the inequality is a formula. To evaluate an expression means to find a numerical value equivalent to the expression. [ 3 ] [ 4 ] Expressions can be evaluated or simplified by replacing operations that appear in them with their result.
Text simplification is an operation used in natural language processing to change, enhance, classify, or otherwise process an existing body of human-readable text so its grammar and structure is greatly simplified while the underlying meaning and information remain the same.
A proof by example is an argument whereby a statement is not proved but instead illustrated by an example. If done well, the specific example would easily generalize to a general proof. by inspection A rhetorical shortcut made by authors who invite the reader to verify, at a glance, the correctness of a proposed expression or deduction.
recursive definition A definition of a function, set, or other mathematical object that is defined in terms of itself, using a base case and a rule for generating subsequent elements. recursive function A function that can be computed by a procedure that calls itself, directly or indirectly, with a base case to prevent infinite recursion.
In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
A current axiomatic definition is that real numbers form the unique (up to an isomorphism) Dedekind-complete ordered field. [d] Other common definitions of real numbers include equivalence classes of Cauchy sequences (of rational numbers), Dedekind cuts, and infinite decimal representations. All these definitions satisfy the axiomatic ...
The examples 1 and 2 denote different terms, differing only in where the parentheses are placed. They have different meanings: example 1 is a function definition, while example 2 is a function application. The lambda variable x is a placeholder in both examples. Here, example 1 defines a function .