Proof by Cases Example + Problem Set #5 - Easy Theory

Here we do another example of proof by cases, mainly in showing that 2n^2 + n + 1 is not a multiple of 3. The cases here are all the "equivalence classes" of division by 3, namely "what is the remainder when divided by 3?" Here, those are 0, 1, and 2. We split the statement up into these three cases, and then prove each one of them separately.

Can this proof be done directly, without cases?

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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.