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**emakarov** The phrase "An equation in x is a statement..." is exactly that — a definition. What comes before "is" is the defined term. The reader is supposed to disregard the commonsense meaning and associations of the defined term that he/she has; instead, a new precise meaning of the term is given after the word "is." In particular, you are not supposed to think that "in" here means "inside." Rather, the whole phrase "an equation in x" is a new indivisible term whose new meaning is given by the definition.

Mathematics recycles a lot of common words by giving them new meanings. We have definitions like "A group is a set with a binary operation satisfying the following axioms...," "A category is an ordered triple...," "A sequence of functions converges almost everywhere if...," "A meager set is a countable union..."