Every math major eventually learns logic and standard proof techniques. For example, to show that a rigorous statement [itex]P[/itex] implies statement [itex]Q[/itex], we suppose the statement [itex]P[/itex] is true and use that to show [itex]Q[/itex] is true. This, along with the other general proof techniques are very broad. A math major would soon come to realize that there are some nuances of proofs that vary among the different subjects. For example, in real analysis, a possible way to show that two real-valued objects are equal is to show that neither can be less than or greater than the other. What proof tips (could be as specific as you'd like) could you provide?