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A term serves as an argument for a proposition. A term may include functions (+,-,x), constants (1, Max, π), and variables (a, b). A term does not form a compete proposition. Accordingly, it cannot express a fact, so it cannot express a relation.

So '(5+a)<9' is a proposition; wherein '(5+a)' is a term, which functions as the argument that saturates the predicate '<9'.

Is the word expression just the most general term for a well formed set of symbols, which could apply to terms, equations, and formulas?

Hal
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1 Answers1

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The word proposition is less commonly used than sentence and formula.

It is possible to use the word expression to denote something that is either a term or a formula. But there is no real need for the word.

André Nicolas
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  • Can expression also be used to refer to the predicate, or to something in the predicate? – Hal Mar 16 '14 at 19:41
  • A term is never a proposition. To make an analogy with ordinary English, terms are nouns or pronouns, while propositions are sentences. – André Nicolas Mar 16 '14 at 19:46
  • Pardon me, that's not what I meant to type. I edited it. – Hal Mar 16 '14 at 19:49
  • Unlike predicate symbol, or term, or formula, the word expression has no formal meaning, so can be used informally as one wishes, if one wishes. It would however be a very odd thing to refer to the very incomplete "$\forall x(f(x)\lt$" as an expression. – André Nicolas Mar 16 '14 at 19:54