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An expression in mathematics is a collection of numbers, variables and mathematical operations such as addition, subtraction, multiplication, division, powers and roots, trigonometric transformations and so on. An expression does not normally contain an equality or inequality sign.

An equation consists of two expression with an equality sign between them. The equality may be true for none, one or more (including infinitely many) values of any variables appearing in the equality.

A function is a mapping from one set to another such that every element from the first set is associated with at most one member of the second, and such that every member of the second set has at least one member of the first that is mapped onto it. The two sets may be the same or different. The mapping may be one-to-one or many-to-one.

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Q: What is the difference between equations expressions and functions?
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