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Alternately, it's a very useful technique to identify the penultimate step; it's often a useful rephrasing of the problem, and gives something easier to prove.
by sdenton4 9y ago
Alternately, it's a very useful technique to identify the penultimate step; it's often a useful rephrasing of the problem, and gives something easier to prove. And then just repeat...
(It's probably usually a hangover from poorly taught rote proof exercises in a lower grade, though.)
- arielb1 9y agoThis is how you do high-school algebra, after all. As long as it is clear that all steps are reversible, it is ok.
- gus_massa 9y agoWriting the proof in the wrong direction is useful in some kind of problems, for example to prove by induction that 1^3+2^3+3^3+4^3+...+N^3 = N^2 * (N+1)^2 / 4. My recommendation to my students is to write to "proof" in the wrong direction in a scratch paper, the rewrite it carefully in the correct order in the final paper checking that all the implication go in the right direction, and then destroy the scratch paper.