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Thus an expression represents an operation over constants and free variables and whose output is the resulting value of the expression. [ 22 ] For a non-formalized language, that is, in most mathematical texts outside of mathematical logic , for an individual expression it is not always possible to identify which variables are free and bound.
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.
An idiom is a common word or phrase with a figurative, non-literal meaning that is understood culturally and differs from what its composite words' denotations would suggest; i.e. the words together have a meaning that is different from the dictionary definitions of the individual words (although some idioms do retain their literal meanings – see the example "kick the bucket" below).
Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.
Normally, expressions and formulas do not appear alone, but are included in sentences of the current language, where expressions play the role of noun phrases and formulas play the role of clauses. Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and ...
The new year will be a busy one in the night sky with celestial sights of all types for everyone to enjoy, many of which can be viewed without needing a telescope or traveling hundreds of miles to ...
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