Question 381306: Can someone explain proofs to me? I have no idea how to solve them at all.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Basically you just prove what the question asks you. However there are several techniques for proving.
Induction - this is good when you want to prove something holds for all integers. To prove by induction, set a base case (e.g. n=1), then show that if the identity holds for some k, then it must hold for k+1.
Contradiction - Assume that the contrary is true, and try to find some sort of logical contradiction.
Direct proof - pretty self explanatory, just show the proof without making any sort of assumption.
Constructive proof - Use this when you want to prove something with certain properties exists.
Bijection - This technique is used mainly on combinatorics problems. Sometimes, if you want to count the number of elements or sets but there is no easy way to do it, a bijection can map this problem to another problem that is simpler.
Proof by exhaustion - done by proving each case separately (often tedious).
In addition, there are multiple ways of expressing proofs:
Paragraph proof - basically write the proof in standard essay form, proving all of your statements. This is the most common type of mathematical proof.
Two-column proof - The proof has two columns, with tabs entitled "statements" and "reasons." You'll most likely encounter this proof in a high school class more than any other type. In my opinion, I dislike two column proofs since it is more difficult to express ideas, and proofs that require unusual logic can be nearly impossible to express in two-column form.
Flowchart proof - The least common of these proofs, done by expressing ideas in a flow chart.
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