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Remember that a proof is meant to be read by someone else; it is not just notes to yourself. That means you need to communicate using standard notation. Suppose that your proof claims that
1 = 2is true. Clearly, the proof must be wrong, since 1 is not equal to 2. But what if, having written 1 = 2, you say that you meant something else. Does that help? No! Remember that you are not there to explain your proof. It must stand on its own. It must use standard notation in standard ways or it is unreadable.
It probably seems odd that I am bringing this up at all. Who would claim that 1 = 2? The reality is that most past students have written patently false statements on homework and exams. When asked about them, students say that they meant something other than what they wrote, and that I should read their mind to understand what they really meant. That will not fly.