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My candidate would be the (internal) direct sum of subspaces $U \oplus V$ in linear algebra. As an operator it is equivalent to sum but with the side effect of implying that $U \cap V = \lbrace 0\rbrace$. Whenever I had a chance to teach linear algebra I found this terribly confusing for students.

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My candidate would be the direct sum $U \oplus V$ in linear algebra. As an operator it is equivalent to sum but with the side effect of implying that $U \cap V = \emptyset$. lbrace 0\rbrace$. Whenever I had a chance to teach linear algebra I found this terribly confusing for students.

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My candidate would be the direct sum $U \oplus V$ in linear algebra. As an operator it is equivalent to sum but with the side effect of implying that $U \cap V = \emptyset$. Whenever I had a chance to teach linear algebra I found this terribly confusing for students.