Philosophy of Mathematics

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If there is a valid expression in mathematics, and if that expression has no solution. Then why is it not considered an error, or flaw within the mathematical construct.

If I were to answer my simple math questions in elementary school, with a question mark. I would fail my test, or homework. Why then is it allowed within the construct itself?

Why is division by zero being "undefined"..... not considered a problem in mathematics?
 

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