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Name: arlene langley
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
A question in a sixth grade text as: An algebraic expression ______ suggests an operation. The book says the answer for the blank is "always." A parent challenged this answer saying that a single variable for instance can be an algebraic expression which does not suggest an operation. Our question: Can a single variable be defined as an algebraic expression, or does that variable have to be tied to a sign such as n + 5? or 2n? Perhaps what we need is a specific definition of expression. Does it mean the same thing as equation?


Replies:
I vote with the parent. I think that you are correct that a more careful definition of "algebraic expression" is required in order to decide this issue. As one of Lewis Carroll's characters in Alice in Wonderland said, "Words mean exactly what I want them to mean, neither more nor less." Definitions in mathematics are up to definer. Least you think this leads to anarchy, be aware that there are standardly accepted definitions which mathematicians agree to but some words have not reached this status. The questions that you should ask are about what is true in light of the definitions you accept. It is widely accepted that algebraic expressions are made up of variables and operations combined according to certain rules of formation (e.g. x+ would not be a valid expression). Single variables are accepted as valid expressions. Note that operations do not have to be binary. There are unary operations (e.g. square root).

chaffer



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