tag:blogger.com,1999:blog-2400513859305780710.post2703963086463535960..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Nonnegativity. Topic: Algebra/Polynomials. Level: Olympiad.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2400513859305780710.post-49007508718562239502006-01-27T14:42:18.000-08:002006-01-27T14:42:18.000-08:00Quick question. What is the difference between in...Quick question. What is the difference between induction and strong induction? Or are they the same and strong induction just sounds cooler?Mattnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-11752463728610760402006-01-27T21:58:51.000-08:002006-01-27T21:58:51.000-08:00Regular Induction - showing that case k+1 follows ...Regular Induction - showing that case k+1 follows from case k.<br><br>Strong Induction - showing that case k+1 follows from cases 1 through k.<br><br>They are similar, but strong induction uses a stronger hypothesis, as the name suggests. For instance, in this problem, I had to use strong induction because g(x) could be ANY even degree less than 2n+2. If I could show that the degree of g(x) had to be 2n, then regular induction would've sufficed.paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-59389778808109990932006-01-28T13:42:33.000-08:002006-01-28T13:42:33.000-08:00P(x) = 3(xy)^2 + 3? Can't be that easy. Or d...P(x) = 3(xy)^2 + 3? Can't be that easy. Or do you mean real coefficients rather than integer/rational?QCnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-76215486841365572842006-01-28T17:04:00.000-08:002006-01-28T17:04:00.000-08:00Uhh... P(x) = 3(xy)^2+3 = (xy)^2+(xy)^2+(xy)^2+3.....Uhh... P(x) = 3(xy)^2+3 = (xy)^2+(xy)^2+(xy)^2+3... So that doesn't work, maybe you read the question wrong. And it's real coefficients.paladin8noreply@blogger.com