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Definition of algebraic expression

An algebraic expression is a collection of symbols; it may consist of one or more than one terms separated by either a $+$ or $-$ sign.

If by symbol we only mean letters such as $a, b$ or $c$, then what about this algebraic expression which consists of only one term $1a$ or $a$? There is only one symbol i.e., $a$, not a collection! But if by symbols we mean numerical symbols such as $1, 2 , 3$, etc, and letters such as $a, b, c,$ etc, then $1a$ is a collection of symbols. I want to confirm what the word symbols is meant to be in the definition; numerical symbols or letters? And want to confirm if $a$ is an algebraic expression consisting of only 1 term.

This is a definition of algebraic expression from the book Algebra for Beginners by S. Hall, link: http://www.forgottenbooks.org/books/Algebra_for_Beginners_1000009092.

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    $\begingroup$ You can have a collection of one element. By your definition above, "it may consist of one or more than one terms." $\endgroup$ – Alex Jul 25 '13 at 16:55
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The definition says that in an expression the terms are separated by a $+$ or $-$ sign. $1a=1 \times a$, so it is an algebraic expression. It is possible to have a collection of just one element- so $a$ is indeed an algebraic expression. Letters as well as numbers are both considered symbols.

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Hope this link:

https://en.wikipedia.org/wiki/Well-formed_formula

will give you a broader explanation/perspective.

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