I understand how the steps in a proof are inferred from other steps that are either given or already inferred. Sometimes though, in previous lectures, a professor would begin proving a certain theorem or equation (such as in calculus and statistics) and then at some point that may as well have been arbitrary to me, declared it proven. What decides the last step in a proof and what about it is so special that it “proves” the subject?
In: 4
The last step is showing the thing that you set out to prove. It is hard to give any more info without context or an example.
If you want to learn about how to do proofs, I would suggest a proofs textbook. Mathematicians spend years learning how to write proofs elegantly and succinctly, but the journey usually begins with topics like logic and set theory. Some math majors begin their studies with a proofs class taught from a proofs textbook.
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